If it was ever possible, what kind of customization would you like to see? Hair colors, hairstyles?
Different faces would be very difficult indeed. In the text game, we had customization for body type (curvy, slender, etc), skin colors, hair colors, eye colors, and some people found it jarring when scenes wouldn't have their custom character so that was the issue. Probably for a 3d game it's a bit easier... Hair colors and hairstyles aren't that difficult and they're not that jarring, eye color can be a candidate as well but anything beyond is a bit difficult.