Persona 3's Tartarus is a very well executed version of the randomized dungeon concept, but it has not quite escaped one of the biggest flaws of that archetype: the lack of plot. Persona 3 is very good at giving the player interesting short-term goals and a sense of making progress into the tower, but it doesn't do quite enough to make that progress a part of the game's story. At times, it seems like the characters themselves do not have a real reason for climbing Tartarus, and that the only reason to go into the tower is to fulfill Elizabeth's requests. Often, it just seems unsatisfying to reach the top of a block, only to have nothing happen.
Just about the only story-related things to be found in Tartarus are the Old Documents, the items found at the top of each block. However, instead of being deep insights into the truth behind the game, they are only small snippets a sentence or two long, and more often than not they are a statement of the writer's confusion rather than anything helpful. Talking to random people in town tends to give better information than the Old Documents, and major plot events reveal far more. What is more, what little information those documents do provide is never even acknowledged by the characters. The Old Documents are among the most time-consuming pieces of information to acquire, yet they might as well not exist as far as the plot is concerned.
In addition, there is not a lot of character interaction in Tartarus itself. Other than the few times where you must go to Tartarus for plot reasons, there really isn't even much in the way of dialog. Sure, characters have all the things they say in battle and when responding to commands, but other than that, the only dialog you see are Fuuka's status reports as you climb the tower, but those are not very much. Most of the time, all Fuuka talks about is whether she can she can locate the next target floor or not, and a lot of that dialog repeats itself over and over again as you climb the hundreds of floors. When you confront one of the powerful bosses near the top of each block, all Fuuka says is that it is a really strong lone Shadow, and nothing else occurs. Even reaching the false top of Tartarus, all you get is Fuuka wondering "is this the top?" with a single sentence, and not much else.
The problem with all of this is that the entire structure of Tartarus, with its segmented blocks and barricades that only vanish as the main plot progresses, is very well suited to having significant plot scenes occur within it. Places like the permanent teleporter rooms, boss battle rooms, and the barricades that separate blocks would all be great places for unusual events to occur. Maybe a boss Shadow would do something unusual, or talk to the character briefly, or attack just as the characters find some clue about the true nature of Tartarus. Maybe the characters could find a room that was originally part of the lab beneath the school that spawned Tartarus ten years prior, and get a glimpse of the events that unfolded there at that time, or maybe find the remains of one of the other Anti-Shadow weapons like Aigis. Maybe reaching certain places would cause Pharos to appear and speak with the hero briefly. No matter what they might be, having even small events like that scattered throughout the tower would go a long way to make trips into Tartarus feel like a more significant part of the game's story.
With all of that said, I can understand some reasons why the game developers chose not to do so. After all, progress through Tartarus occurs somewhat independently of progress through the main game, so events would be almost impossible to synchronize. Further, the characters available to you for any given trip to Tartarus can vary greatly from day to day, and characters getting sick or tired affects that even more, so it would be impossible to create events that depend on the presence of a particular character. However, these problems are not insurmountable. In fact, the entire Social Link system shares the synchronization problem and was still implemented well enough. That problem can be overcome for Tartarus with the same solution that helped the Social link system: keeping the different plots isolated from each other. Have the events in Tartarus depend to a reasonable extent on the events of the main plot (based on the barricades), but don't have events in the main plot depend on what happens in Tartarus. In such a case, Tartarus events and the character interactions inside would dictate how much the characters actually know about what is going on, and discussions of "where do we stand?" and "what do we do next?" would mostly take place there. Balancing all of that might require a lot of planning, but it is possible.
The other problem for putting events in Tartarus, the unreliability of characters, is not that unusual of a game design challenge, so it is actually less of a concern. There are at least two characters who are always present in Tartarus trips (the hero and Fuuka), so there will always be some kind of reliable basis for character interaction and events. Beyond that, it is a simple matter of changing scenes slightly to reflect who is available, something that occurs in a large number of games and often makes such games a bit more interesting. Having a few more scenes that might change depending on who is present would add a bit more variety to the game.
As it stands, it seems like a glaring contradiction in the game that the character's stated reason for entering Tartarus, a desire to learn more about the Dark Hour and find a way to stop the Shadows and end the threat of Apathy Syndrome, is the one thing that does not happen at all in Tartarus. Far too often, it just feels like exploring Tartarus isn't important.