See, what I kinda liked how the dungeon crawling was kept with only Tartarus because I feel it works in accordance with the narrative, the story the game wanted to tell, but also with how the gameplay itself actually contributes to its underlying message -- Tartarus, in Greek Mythology, refers to the dark netherrealm, where Zeus banished the Titans and his father Cronos, that is to say the Under World. In Persona 3 it is shaped as a giant and fightening looking tower, where Death awaits at the top -- It is quite litterally the gateway to hell.
It's also noteworthy to mention how as it being this gigantic tower it symbolizes never-ending journey of life that all the main characters are going through -- They strive to find meaning with themselves as they com-bat the shadows. It's also important to note that while one can argue from a gameplay perspective that Tartarus doesn't change overtly much to warrant an interest, it does change in its tone and sense of eerie alien-presence it carries when venturing further and further up, the tone shifts as the main characters come to realize the hopelessness of their situation, the music changes and becomes almost more somber.
Tartarus also relates to one the main aspects, which Persona 3 takes into consideration, something that is shared among most games -- The concept of 'time'. Death itself is a physical present character in the game, while from a antropological standpoint it is also a subject that features prominently into the backstories of its characters -- But above that there is 'time'.
"Time is something no one can escape. It brings us all to the same end". ~ Pharos

In relations to what Pharos says at the beginning of the game -- Persona 3 heavily lays itself out in accordance with time, you spend most of your time in the game trying to allocate time and effort into different objectives. The game doesn't utilize time as a form of punishing the player or telling you to hurry up, but rather as a way of 'framing' your experience to make you stop and consider your choices.. It doesn't punish you or place judgement upon you but it sits and watches -- Like a very curious philosopher, it seeks to understand, not just from a plot-perspective, but also from a player perspective, what kind of person you are. In a way, it profiles you.
Basically, we have to consider that time is something which is explored in the gameplay, whereas death is explored in its narrative.
The conclusion we can draw from this is that the relationship between the game's mechanics and its narrative will lead us to understand that the narrative itself might be a smaller subset of the overall mechanics the game presents itself with. Other games have done this intentionally, like Silent Hill 2, where the narrative isn't as much dialogue or cutscenes, as it is weaved into its gameplay mechanics in a somewhat symbiotic relationship.
I think this is where I need to move to my next point. If you take an example -- Boot up let's say.. Knights of the Old Republic 1, for instance! The Endar Spire is under attack it's about to blow up -- Don't do anything. Nothing.. the opening cutscene heavily implies that the ship you're stationed on is about to blow up and crash into that nearby planet, and yet.. nothing happens? Now do something else -- Play Super Mario World for instance, wait a few minutes and watch Mario die of cardiac arrest as you left him to his own shenanigans. You monster. One answer is that there's a starching difference between the kind of the games they are -- One is an RPG the other is a platformer, in other words one is more heavily reliant on narrative agency, where the story is carefully driven by the player, at their own pace, whereas the other is gameplay-centric.
It give us an understanding of how time plays pretty much into any game but with different approaches. The fact that our example of KOTOR 1 is a story-driven game is what makes the hours of negligence in-game irrelevant on its in-game time clock. The game will only truly progress at the player's behest no matter what. Time itself is measured by plot events that are initiated entirely by the player him/herself. Defeat two Sith troopers in combat and you've basically advanced forward in accordance with the game's timeclock. It'll only follow your actions, step by step. If we were to take another example, for instance, we could take BioWare's Dragon Age Origins. One might have noticed that as you advance the plot in the game, once you've done a certain amount of stuff in the game, you can talk to the party and they'd refer to how over a year has passed.. But how did that happen? You as a player couldn't possibly have managed to calculate how it functions, because it only works when you make the choice of advancing the story. You could have decided to spend 7 hours of doing nothing but grind, or spend less hours and gotten to the same point of the characters saying "A year has passed".
The other school of time is where games like Mario falls into -- Where time is dictated by an AI within the game's mechanics that tells you to get your ass in gear, you 'll lose the game. Time progresses alongside real time to create a sense of urgency. It's of course important to note that not necessarily all games fall into either category, some uses a conventional mix of both to craft unique experiences, like Majora's Mask for instance, where you only have a limited amount of time to save the world from ultimate destruction.
I think the major point though of Tartarus has basically been summed up so at this point I'm just rambling.
To keep a long story short now -- I think that what Persona 3 does, with its time progression and Tartarus, is creating a sort of intrigate discussion on time-progression in gaming itself and how much it weaves into the narrative. If the player chooses to explore Tartarus, the game switches over to Tartarus Time, in which the progression of time is automatic, and is represented by hours rather than days. This is discreetly communicated to the player in two major ways. First, the arrival of the Dark Hour is heralded by the appearance on screen of a giant clock, which strikes midnight before falling apart. The automatic progression of the hands of the clock indicates that time has begun to move on its own, and the collapsing of the clock indicates the destruction of the previous model of player-dependent time progression. Second, the entrance to Tartarus proper is through a door embedded in a massive clock. The clock represents the thematic “minimizing” of time- from Iwatodai’s days to Tartarus’ hours- and symbolizes that unlike in Iwatodai, in Tartarus every minute counts.
(There are also several more subtle examples of the game suggesting that time moves differently in Tartarus, or that Tartarus’ time is measured in minutes and hours instead of days and months like Iwatodai Time. For example, in the opening cinematic, the main character is staring at a large clock when he experiences the Dark Hour for the first time, and the transition from Iwatodai Time to Tartarus Time is marked with a shot of the character’s MP3 player, which measures time in mere minutes and seconds. The FMV introducing Tartarus also reveals that the structure itself is covered in several large and sometimes irregularly shaped clocks, although it can be difficult to make out since the scene is so green. Shinegori Soejima’s concept art clearly depicts Tartarus as being decorated with at least thirteen massive clocks. You can also get a taste of the two time streams colliding if you go on a date with Elizabeth. The Velvet Room is governed by Tartarus Time, as evidenced by the giant one-handed clock looming over Igor’s desk, but Elizabeth can actually leave the Velvet Room to explore Iwatodai. Choosing to go on a date with Elizabeth will not advance time, even though selecting an activity is how time is advanced during Iwatodai Time. Elizabeth is governed by Tartarus Time, so her progression of time is automatic- just because the player has selected an activity, and in so doing has explicitly decided to advance time, that doesn’t mean anything to her. So, you get to engage in an activity without progressing time, thanks to the presence of Elizabeth.)
And blah, blah, blah..