I like that idea of him shedding his persona. Maybe giving the player the option to outfit him in his old train robber clothes. But he looks cool as the ninja. Another part of the game that id be interested in seeing retold was the hidden underground castle where you learn of the fate of Raiden/Odin

This is still my favorite FF game. A remake would be a dream come for me. With so many playable characters and arcs, this would no doubt be a massive undertaking, but I needs to happen. As for your ideas to expand upon character arcs in a remake. SPOILERS AHEAD.

I would literally expect that, some of the characters like the Yeti and the Mimic guy didn't even have a story at all, though the later was more like a bonus toon. I'd expect even those lesser characters to have a small arc and the main cast to get more shine. As for Shadow, I did feel confident that Relm was his daughter, and Strago was his father or would be father in law. If i remeber correctly at the end credit scenes, Shadow has a scene with Strago helping him flee Kefkas castle and referring to him as "Old man".

A proper remake could do wonders for the story and shed more light on the background and future for all the characters.