I guess I am in the minority here. I don't think that the Four Warriors of Light need to be fleshed out. I mean, maybe it's because FFI was my first FF and while I love the way the series has evolved the first FF was a different kind of game. Your warriors are supposed to be nameless because it is about your choice. You choose the name and job class.

I would definitely play a re-imagining though. But I think instead of trying to make FFI like later FFs, that they should soup up what is already there. A dramatic graphics overhaul is a must. Maybe there should be more job classes and abilities and greater visual customization of your characters. It would be like a Western RPG exceptyou get to customize FOUR characters :P The world would also need to be expanded and made more interesting to fit with modern times, as the original is a very simple and short game. In conclusion, a re-imagining would be like an open world Western RPG, but with improved turn based battle system and a JRPG art style.