This is an age-old discussion. However, it could lead to identity theft, which was mentioned in Wizard Weekly. Apearrance is one of the few ways to tell between people with the same name, so this could lead to impersonation.
I don't see how this can result in any kind of identity theft. It's not like they're changing their username or in game name. There's only so many hair, face, and skin tone combinations, so it's not like there aren't already a few wizards around the Spiral that look like you. I think the problem is in the fact that you're supposed to look like you. You can change your hair color and style, but you can't really completely change your face without some heavy-duty magic.