What you consider to be an RPG, and why and how people should be playing them is more like an amalgam of two different styles of RPGs, rather than a good or accurate definition of the whole medium. You don't give much explanation or justification for your opinions, but rather you've made two distinct propositions, and then just extrapolate and explain them in a great detail. I cannot detect any evidence or reasoning for these base assumptions themselves, which you seem value as axiomatic. However, considering the whole gamut of released RPGs from 1970s to this day, how people have played them and what different people and game designers have consider to be a role-playing game, I strongly disagree with your normative assertions. Since the normativeness in your advocating for your preferred style is osmium thick, I'll try to explain my understanding of the whole issue in a very thorough manner (brace yourself for the mother of all TL;DR / Wall of Text postings). Issues like what different styles there are, how these differences were born, why there are differences and most importantly why there isn't any particular well defined "true" form of role-playing, but various different styles, preferences and goals. These styles sometimes contradict and exclude each other, but more often overlap in single RPG system or game.
There isn't much widely established terminology or a rigorous theoretical framework for RPGs, but regardless there's some consensus on what all these terms mean and represent. I've also seen people using terms such as a school of thought, goals, preferences, movements, paradigms or categories of engagement interchangeably to a style. Roughly, a style in this context means full group contract which includes every facet of how the game is played or what is expected from it. It's not necessary any explicit verbal or written agreement between participants, but more like a general and often unsaid understanding of how the game is played all-around. Not just the mechanical rules or a designer intent, but also how scenarios are constructed, what can happen in-game, what kind of behavior is expected of PCs, how actions not covered by the rules are resolved and so on.
What you are describing as playing an RPG is referred in an RPG theory jargon as simulationism (this seems to be your main thesis, although you add hints of immersionism to it). Other styles are referred as narrativism / dramatist and gamism. Sometimes immersionism is considered as a part of simulationism, but sometimes it's consider as a separate category. Lines are blurry and opinions vary, and distinctions can be made ad infinitum (e.g. some people have suggested categories beyond these such as Social or Explorationism, but the aforementioned three are most widely recognized in a form or another).
Here is a brief descriptions of these styles:
-Narrativism: values how well the game creates a satisfying storyline. It's not catered to any specific taste or subgenre, everything from believable gritty dramas, or purposely comedic and over the top pulp action games can fall into this category. Often results for gaining a good narrative are more important than strictly following game mechanics or methods of playing. GMs are expected fudge with dice results if the story requires it (the GM not counting a critical hit roll, if it would kill PC in an unsatisfactory situation for the narrative). Players can be allowed to have a lot of leeway for making up in-game details, for framing scenes or even having limited control over certain NPCs (a player doesn't necessarily need a confirmation from GM whether an inn has some particular wine his PC wants to order, if it helps to make the scene more as player wants to have, in order to create a better narrative). Systems which purely focus to this style tend to have light, abstract and minimalistic game mechanics. There can be predefined narrative conclusions and conditions for the game regardless of any player action, and players are expected to pursue these (e.g. a pre-set goal that all the PCs are supposed to die at the end). Roles, authority, and responsibilities between GM and players can be blended in plethora of ways. Often tries to emulate some specific non-RPG genre or style (from film, literature, etc). Examples of systems which heavily lean to this style are: The Mountain Witch, It Came From the Late, Late, Late Show, Dust Devils, Primetime Adventures.
-Gamism: values a fair challenge for the players, and not just the PCs. Often there's some predefined goal or victory condition, which can be achieved or failed. PCs can expect to be rewarded from succeeding in-game challenges (loot, XP, etc), despite in-game believability or consistency (looting gold coins from corpses of wolves). Encourages balance between PCs . Challenges can be resolved through game mechanics or freeform; winning an ogre in a brawl through character abilities is equally valid as resolving a worded riddle with player's wit. PCs can expect to survive as long as they act properly within the given game context, but there should always be possibility of failure if PCs muck it up, regardless of in-game consistency or dramaturgy (this should be rooted in a scenario design at the core level, and to the system design through mechanics such as challenge rating / scaling enemies to a PC level). Location where the game happens can be confined to certain narrow area, like a dungeon, from which leaving is considered as an end of the game, defeat or loss. Keywords are fairness, balance, teamwork, challenge and victory/defeat. Challenges can be pretty much anything, from intellectual mysteries to verbal debates and tactical combat. Examples of systems which heavily lean to this style are: Dungeons & Dragons, Stormbringer, ORS games. Most CRPGs and earliest RPGs are heavily oriented to this style. Also the line between these games and certain board games like Arkham Horror or Heroquest can be very thin.
-Simulationism: values resolving in-game events based solely on game-world considerations, without allowing any meta-game concerns to affect the in-game decisions. Thus, a fully simulationist GM will not fudge results to save PCs or to save her plot, or even change facts unknown to the players. The style tries to eliminate or minimize most meta-game concerns from affecting in-game events, and tries to maintain a self-contained world operating independent of player / GM will or preferences (be it drama or game related). GM is not supposed to steer a game narrative or plot to any particular direction, but rather just maintain her in-game world and let players do whatever it is what their PCs want to do, in limits of what is plausible by in-game logic. Such a GM may use meta-game considerations to decide meta-game issues like who is playing which character, whether to play out a conversation word for word, and so forth, but she will resolve actual in-game events based on what would "really" happen. A strict separation between GM and player roles is typical. a GM isn't supposed to violate player agency, unless there's explicit in-game reason for doing so. Be it guiding or changing rules or in-game facts in order to accommodate game, narrative or PC's immersion needs. Simulationism isn't necessary concerned with simulating reality, but it can be a simulation of any fictional reality, world or scenario, as long as it is consistent with itself. Examples of systems which heavily lean to this style are: Ars Magica, HârnMaster, Middle-earth Role playing (had to mention this one as it's the very first RPG I ever played).
-Immersionism: This is not similarly all encompassing style like three previous ones, but something between a stance from which players should do their in-game decisions to a game focus. Shortly put valuing players immersion to his PC above everything. Often more associated with LARPs. Sometimes conjoined with simulationism in goal of making in-game decisions by only in-game information and considerations. Still, immersionism is sometimes conflicting with simulationism because of player limitations (can a person who doesn't know anything about geology truly immerse to his PC who is a geologist compared to a player who actually is a geologist. A pure simulationist GM will not notify any meta-game considerations like a player aptitude, unlike an immersionist GM who might fudge the rules, rolls and actions to help a player to immerse to his PC and produce more believable results in accordance to what kind of a PC the player is trying to immerse to). Example of system which heavy lean to this style is Vampire The Masquerade.
Here's an example of how a same sequence could be play out according to these three different styles: PCs want to acquire a ring, which is in possession of a peasant, who is living in a village, which inhabits hundred peasants in total. The only way to achieve this is to go through all peasants individually.
The narrative approach will favor making decision based mostly on what is subjectively good for the story. If DM wants to highlight all the time and effort PCs must do, he might dictate that PCs must go through at least eight peasants before the ring is found. If he feels the story is dragging, PCs might discover the ring in the hand of second peasant they meet.
The simulationist approach in a other hands favors that GM has decided which peasant has the ring in advance according the in-game logic, and PC can choose what order they search peasants. They might find it immediately on the first peasant, or they might need to search 99 peasants before finding the one. There can be clues for which peasant has the ring or they might not be. This is solely according if it's appropriate for in-game reasons, but PCs cannot count that there's anything to make the task any easier. If in-game reasons determinate so, it can be possible that PCs cannot find the ring at all, regardless of their attempts (e.g. during the second day of searching, the GM will roll a 10.0 MS earthquake from a randomized weather table, and the ring disappears from the face of the earth).
The gamist approach can be either way, but there should be available clues or crutches for players to find, if they are clever enough to discover them. This can be totally regardless of in-game logic or whether it's called for storywise . Or GM can be persuaded to change preplanned in-game narrative, if players came up with enough good idea to ease the task, or perform miraculously in some other way.
In almost all systems and games, these styles often overlap greatly and contain elements from every single style. Despite sometimes contradictory goals and conflicting results. A system might be gamist in some area such as a class balance between PCs, but pursue simulationist goals in everything else. Then give a GM an absolute fiat to supersede everything in-game related while advising GMs to bend rules and sacrifice in-game coherence, if it provides a fun and entertaining story for players. However, these goals are not constantly at odds, and individual preferences are in all cases I've encountered mixture of all these. People tend to point out inconsistencies only when they want to rationalize their disapproval for something or win a debate on the internet. Some dissonance seems quite natural in a complex phenomena like RPGs are.
Here's links for some choice quotes from some RPG books I happen to own (all of these are RPGs without any doubt. AD&D first edition, Call of Cthulhu, Pyöreän Pöydän Ritarit, HârnMaster, D&D third edition, Hero System). These quotes tell how these games define what is RPG and themselves, and how GMs should run their game and players play their PCs. As you can see, it's impossible to parcel any singular RPG definition, which is at same time detailed, categorical and logically coherent with itself. Neither can you piece out any normative way which is the real way to play RPGs. Even from this small sample of RPG systems, let alone considering every system which been published and how millions of people have applied these vague guidelines during last 40-50 years.
Like most complex social phenomena, RPGs were not discovered in a similar sense as chemical elements were found. Neither they were exactly consciously invented either (nobody ever just sit down, and said "hmm, I'll make this new game form which will be called RPG. It'll be all about players immersing their characters, and it'll be the definition of what the game is all about now and for all eternity"). Metaphors like growth, evolution, emergence, branching of a tree are more appropriate to describe how RPGs came to be, and what this hypernym consist of.
If I am to explain the RPG history briefly without being too anal about it, it would be something like this: First there was war games, which were and still are comparable to miniature games and strategy orientated board games. Due experimenting and tinkering several people invented variants to this, in which the basic unit of play wasn't an army to command, or a platoon or squad, but an individual person. This shift wasn't that radical at first, and there wasn't much focus on immersing or "roleplaying" this avatar. These games were still played and had objectives very much like all other wargame variants (I guess, at that point it would've been comparable to immersing yourself to your Monopoly piece).
The next step was the idea that maybe you could keep on playing with the same character through multiple different games. From that there wasn't a big jump to consider that maybe this single character got better at what he was doing (fighting), and the gear he acquired would persist throughout different game session. These characters started to have simple histories, so suddenly there's a narrative. Naturally at first these stories were rather simple, more like annals of different vanquished enemies, loot what was gained and battlefields and rooms which were explored. Still gradually these started to get more complicated and complex, questions like what happens between the battles started to emerge, and why and what for these characters were fighting. Along appeared supporting characters you didn't need to fight against. Rudimentary plots, and a larger concern for the setting in which games take place become more significant.
This process was quite far ahead, when some players started perceive games more and more from the perspective of their characters, and acted according what they thought their character would react rather than what was merely tactically advantageous for succeeding in the game. Like narratives before, this focus to a character immersion crept to these games. Naturally during all these steps, there's been schisms between players about what was right and truest way to play these, and how players were supposed to play these games. No singular goal become dominant, and usually games tried to adopt something from all these different standpoints (game, story and immersion), in various different relations. Some regarded consistency and had clearer designer intent than others, but mostly it's only very contemporary design, which produces games which are absolutely focused on a singular style.
Then some people started to consider that maybe this game model could be used to emulate certain literary works, TV-series, movies and so on, instead of fighting enemies and exploring dungeons. This was followed by certain games starting to focus on simulating these fictional settings as accurately and realistically as possible. Afterwards some games elevated exploring inner workings of PCs as their primary goal.
This could go on and on, as this branching out continues even as I am writing this. RPGs are not about being faithful to some grand original idea or principle (there isn't one). It's rather this long continuum of all these styles, countless different systems played and applied by millions of different people. All which have evolved by experimentation, tinkering and usually through very gradual changes over the years. In this context (or any context really) evolution shouldn't be mistaken as a progress towards something "better", older games and ideas do not necessarily become obsolete and many different styles co-exist side by side. Hell, one of the oldest RPGs is still the most popular one.
Propositions like "player should always base their decisions on what their character wants and knows", are arbitrary declarations, because the format was never based around anything like that. The format can played from different stances besides that. Although I can somewhat understand why these are being thought, and I can even guess some reasons for that, but in this instance I will refrain from guessing why Sylvius the Mad has reached to the conclusions he proposed. Rather I will post the best model I've encountered so far, which tries to categorize different stances the player may take in making decisions for their character (the model is made by Ron Edwards).
Actor: Decides based on what their character wants and knows
Author: Decides based on what they want for their character, retrospectively explaining why their character made a decision
Director: Makes decisions affecting the environment instead of a character (usually represented by a gamemaster in an RPG)
Pawn: Decides based on what they want for their character, without explaining why their character made a decision
How one values each stance, or what kind of games they produce is a different discussion altogether. But I simply cannot find any intrinsical reason why one stance would be the "true RPG" while others wouldn't be, despite my own preferences.
If I had to make an educated guess, why there's so much variation between RPGs and why nature of RPGs is so divergent. I would attribute it to two different factors. Firstly, from the very beginning RPG systems have emphasized and encouraged participants to change rules, make their own content and goals, adapt, apply and create. This hybrid nature of the form is quite unusual, in which participants server both creators and audience. Secondly is a relative isolation between different RPG groups and players. The format produces isolation between different groups, and groups sizes themselves tend to be small compared to other mediums. Humans being conformist learners, isolation tends to breed diversity in the every field of life.
The very thought that there even could be some "true" RPG for us to find or reason, is either childish reification or some bizarre essentialism nonsense. Still, I believe we can form better categories, and clearer abstractions for this hypernym, but so far the best definition I've found for an RPG is following:
"A role-playing game is what is created in the interaction between players or between player(s) and gamemaster(s) within a specified diegetic framework."
It's best because it's categorical and logically sound, but unfortunately it's not very detailed in a way that it tells us about anything about any particular system, style or game session, nor cannot much be deduced from it. It doesn't operationalize well in that sense, but for something that is large, wide and dynamic as RPGs are, it's probably as good as it's going to get. I don't think this is exactly because of any malarkey, like "we just cannot agree on terms here" , or any other coordination problem between people.
These problems are almost always prevalent, when talking about any large concepts or groups (be it people, what people do, or etc). Especially when they are abstract and dynamic. If we are talking about something which is related to hundreds of thousands or millions of people, to me it is quite obvious that in almost all qualities we are comparing or measuring, there will be a wide range. While discussing or describing these large group-level matters, it tends to be so much more fruitful to just talk about distributions (how things in general are), rather than arguing about some two-valued logic statements, based on whatever concealed BS value judgments.
Conceptualisations, abstractions and boundaries between concepts are always going to be somewhat arbitrary (for numerous reasons, but I'll refrain commenting on them, as this is become more and more irrelevant to the subject).