Fire Emblem has an option to let the AI move for you, but I think it’s only for actually moving troops quickly across the battlefield en masse, I don’t think you can have the AI attack for you.
People can play the game how they want, but only controlling one character in a party turn based game? So let’s say you have a party of 4 and are facing 6 enemies- you will take a turn 1/10 of the combat sequence. How is that fun? Normally you would be strategizing and planning during the AI turns, which are pretty quick. But if you only control one character you will just be sitting there looking at your screen.