In my time playing, I have grown bored of my character's look! I want to be able to visit a barbers to change my hairstyle or use some amazingly illusive and mysterious (but not hard to access) magical shrine to alter my character's face and body. Adding the dye station was a big leap to this customizability I know everyone longs for, but it's just not cricket! (awesome English metaphors).
Without a change like this, in order to play as someone new, players have to create entirely new characters and go through all of what they have already again. It seems like such a minor thing yet impacts so much. Maybe, you could model it off the skill reassignment system; pay a little to change your skills. Hell, it could even be a dwemer plastic surgeon or a daedric deitie of vanity! Just something that adds that flair of flavor.
Much love




PS: You might want to look into a divorce system....