You give a vague scenario of a game, and your argument is that this is problematic for the balance of the game. How can I possibly work on a counterargument when your explanation is that the jack of all trades may be inferior to the build that specializes in 3/5 for a particular fight. I need to know what these stats do, what other abilities exist in the game. I only know of a single game that features a concept based system and the attributes affects the build a lot, Original Sin, but every skill you pick at the character creation explains in GREAT detail what effect attributes have on it. If you decide to not pick the right attribute then that's the obviously wrong decision without any need for debate. It's even highlighted with big numbers saying that "According to your x stat, the skill has y% chance of succeeding". Also attributes are useless for any other kind of interaction in the game.
For every other that comes to mind it just doesn't matter. You can go jack and still be effective. Not as effective as an optimized build, but that's true for any game, with classes or classless. If there is a classless game that if you go jack you can't beat the game on default without any indication that you did something wrong, then that's a bad implementation. But I sincerely can't think of such a game. If you can by all means make a reference.
I honestly don't understand how your example works. It assumes that the stats are the only thing that is important and work a certain way. To illustrate what I mean, let me simplify it even more. If a class has 2 stats and decides to focus on both of them, will it have problems against an equal power enemy that focuses on only one? The answer varies, it depends on what these stats are. If they are offense and defense, they may be equal. If they are offense melee and offense ranged then most likely the enemy will have an advantage especially if there is no way to avoid his damage through a certain gameplay feature. Will the jack be better at dealing with most common enemies than the specialized? Depends. If by specializing means that most enemies die very fast, then it can work better than a jack.
You say that in your example the jack deals better with most common scenarios. How so? What is the quality of the jack that makes him better again most scenarios? If I don't know the quality then I can't know why this same reason makes him weaker against a certain encounter.
Let's take examples of games with a classless system. In Shadows of Mordor a specialized character deals better with common enemies and an all around character deals better with bosses because enemies just die to overwhelming damage but bosses have immunities. So if you focus only in archery, then you won't be able to use it against a boss immune to archery and these are common.
Skyrim and Fallout are the same. A specialized sneak attacker with lighter armor and a high damage/low dps weapon melts common enemies like butter. But for the scripted fights where he can't use stealth, his specialization is useless. It would be better if he was all around and could switch to heavier armor and a higher dps weapon.
In Original Sin depends on the abilities you bring. There are a few clear cut abilities that deal with common enemies which don't work on bosses that well. High damage per turn and flooding the battlespace with summons works for every kind of encounter. Wasteland 2 high damage per turn is paramount. The real difference comes in form of armored vs unarmored enemies. It depends on the encounter. This is true for bosses and common enemies and it's the closest one to your example.
The connection between all these games is that basic attributes and choices you make at character creation, while can affect the experience, are obviously secondary to the skills and gear that your characters acquire during the gameplay. The only way to know how to best specialize is by playing the game and taking note of what works and what doesn't. Sneak may have it's shortcomings in Skyrim, but if you identify them (like for example dealing with dragons), and level archery then you can deal with it. In original sin, having a party that sacrifices durability for raw damage per turn has obvious weakness against encounters where the combined damage isn't enough to deal with the enemies before they come close. Go to the vendor and get some summoning spells. Voila.
I'm not making excuses to avoid talking about your example. I need clarity. That's why I make references to games that already have these particular features. Cause I can use their numbers and features as a platform to base my argument.
Do you know any game that works the way you describe? Cause I don't. And even if we accept this example as valid, then what is the problem of having some builds being stronger than others. This is true for EVERY POSSIBLE GAME in existence. Hell people did whatever builds in DAO for roleplaying purposes that weren't capable of even beating normal and it's supposed to have some semblance of structure. A guy made a rogue that wielded a shield. That's it. Ask those people what would they prefer, a structured system or a completely free one to do whatever they like? After all Dragon Age games were never balanced. I don't think that they will start being balanced now just because the devs said so.
I said fallout is the example that is more relevant because you focused on Skyrim. Skyrim doesn't feature anything that you described in your example. I also explained why I think that the oversimplified system you presented doesn't have to be so because a lot of games that feature classless systems move away from stats and attributes other than the very basic ones like health and action resources or keep them only for roleplaying purposes, disconnected from the actual combat
I feel this goes in circles. Bottom line, if you can give me an instance where your example is valid, either with made up numbers of using another game as an example, I'm more than happy to discuss it. But I can't discuss it if the only mechanics presents are some vague stats and the player can choose to be jack or specialized. It just doesn't work that why. This is your assumption, that an all around build works well in most situations. This is false and every example I brought up reinforces this. If this is cherry picking then so be it but honestly, I don't know many more classless systems that were released these past few years and most other games with the concept either use alternate mechanics (fps for example, deus ex/farcry) or use a modified d20 system. Only Jade Empire has a classless system and still doesn't work the way your example does.