I would be on board with some customization. Not a character from scratch though. But if they allow tattoos, let us pick what and where. If they want different clothes, let us pick them. And they can build them into the story rather than the traditional build a character before you start a game.
I think most fans would have no problem with Cole's look being able to evolve as his powers and tendencies do. If he's good, maybe he unlocks a nicer clothes shop and a barber shop. If he's bad maybe a grungier more underground fell clothes and tattoo shop and a different barber with different styles. It would really make us feel like he is evolving based on the actions he takes rather than BAM he's all different, new voice, new look, new clothes, new style, essentially a whole new character.