I can see changing minor things like hairstyle and things like that.
Otherwise totally changing your appearance should get a reaction of "who the **** are you?" Or "what happened to you?"
Well, the Disguise Self spell already creates that weirdness. People react as if you've always looked that way - and always been the race you're disguised as.
As to the core of the thread, being able to make changes would be nice - particularly for hair/makeup/tattoos - but I land on the side of "the game as released has MUCH bigger issues to work out".