If there's one thing Persona 3 needs in a potential remake over ANYTHING else, is to make the battle UI like Persona 5's.
Just think of the speed of doing basic actions in P3 vs P5. Let's say you want to switch Persona's and use Agi:
In P3, you start on Attack, so if I'm not mistaken that's 4 times you have to press up, then hit X, then if you want to see which Persona has Agi, you have to hit Square, then you can use R1/L1 to scroll through your Personas, choose one, then go back to Spells and use Agi.
P5, hit Triangle, R1, R1/L1 to cycle through your Personas, X, choose spell. That simple, and it's super quick.
I think it's most noticeable when you're fighting against one stronger enemy with an elemental weakness, and you have a Persona to exploit that, as well as at least one other party member that can. In Persona 3, it's so slow to cast the spell, then you have to wait a few seconds before the dialog pops up for the all out attack.
In Persona 5 it's spell, they're knocked down, very brief animation of Joker pointing his gun at them, hit Triangle for All out, unless you want to negotiate or back off. I remember a handful of miniboss battles in P5 like that, where I was quickly doing All Out attacks where I could get a few off in the amount of time it would have taken to do one in P3 or P4.
Also SMT Switch should take notes from Persona 5 on battle UI stuff. It doesn't have to be all stylized like P5's, but make it fast like it.