I believe your agi stat determines the turn order of battle. If you happened to have swapped a persona with low agi previously, you'll have a late turn next battle. Some enemies hit dangerously hard especially if they crit, such as those knights on horseback or those tanks. It's handy to keep a persona that's resistant to physical damage for those types of enemies (ex. Oni level 30 has phy resist.) If you notice you're on a floor with those types of enemies, keep that default or a high agi persona so you can switch first turn.
Welcome to one of the basic RPG conundrums: Do I keep leveling my starting crew or use new characters? Personally I like variety

Besides that, they have different resistances that are better for certain floors/bosses. Higher social links give them unique traits in battle. They have different special moves with unique traits like Chie's galactic punt. Plus, in a way it's cheaper because if you find a great weapon for Kanji, for example, you can just upgrade his armor and switch him in instead of having to buy all new weapons for your same default crew.