I believe I have briefly touched on this point earlier, but Persona 3 FES is a game where it is not advisable to pick a small subset of your allies and use them the whole game without ever using the rest. The main reason for this is simple: every character has unique strengths and weaknesses that can not be ignored. Partially, these strengths and weaknesses are explicit elemental attributes. Yukari is the only ally who uses Wind magic, Wind magic can hardly hurt her, and she will be badly hurt and knocked down by Lightning magic. Akihiko is the only Lightning magic-user, he won't be hurt much by Lightning, and he is vulnerable to Ice magic. Against any enemy who uses Lightning magic or is immune to wind magic, Yukari is a poor choice compared to Akihiko. If there are a lot of enemies around who are vulnerable to Wind magic, then Yukari almost becomes a necessary choice. All of the characters in Persona 3 are specialists. No single character can do everything and fight every battle, and I like that about the game.
There are four important factors at work that I like regarding the characters in Persona 3.
1) Every character specializes in some way. This is the most basic and central factor of this. Each character specializes, with both strengths and weaknesses. No single character can do everything, and every character can do something. Any videogame that allows multiple characters must have some element of this, or the choice between different characters becomes shallow and meaningless.
2) Every character's specialization is unique. This is one of the most important ones. No two characters are identical in role and ability. Any point of similarity between two characters is balanced out by a way in which they are different. Every character has a unique way to fight and contribute to the team. The lets characters have a memorable identity reflected in the game mechanics, so characters are individuals rather than faces and names added onto generic shells or copies of a limited set of archetypes.
3) There are many ways to build a team that can do anything. While this doesn't apply to attack elements, every character does have a focus that overlaps with other characters. Junpei and Aigis are very different, but they both have buffing spells and a variety of powerful physical attacks. If you need to use physical attacks, you have a choice between the two of them. Yukari is a stronger healer and Mitsuru is a stronger magical attacker, but both can heal and use magic attacks, so neither is strictly necessary. There are meaningful choices to made regarding team members, but it is not so inflexible as to force you to use a limited set of "good teams". Instead, you only need to worry about whether individual characters are good for particular situations or not, and can mostly leave the rest of the team up to preference.
4) There is no way to build a team that covers every weakness. Unlike many RPGs, where elements are always constructed in opposing pairs that are both strong and weak against each other, characters vulnerabilities are not based on their strengths. To compare, in Chrono Cross you can always build a team so that you have one ally who is is resistant to fire and vulnerable to ice and another ally who is vulnerable to fire and resistant to ice. In such a case, weaknesses balance out, so any time one character is in trouble, there is another character who is in no danger at all who can pick up the slack. Because vulnerabilities are asymmetric in Persona 3, and because there are an odd number of allies, there is no team that can have resistances and vulnerabilities balance out as nicely as they do elsewhere. There is always an element that can be used against the team that will do extra damage against someone and normal damage against every other team member. Because of this, there is no team that can survive against every possible encounter.
RPGs that allows you to pick a team from a larger pool of characters, yet still has all of these traits, are rare indeed, even though I consider it to be one of the best ways of designing a game built around a team.
Anyways, I should mention that everything I mentioned above is not quite accurate, since I am making a deliberate omission: the main hero. If you add the main hero of the game to the mix, it changes things slightly, but that difference is a topic for another day.