It wouldn't be funny if you got permanent visual changes (scars etc) all over your body when you got hurt. And face full of stitches and bandage.
What has happened to you? A battle against a dragon again? Umm...No, I accidentally bumped my head to a wall too many times when I was drunk.
Edit: I don't support changing your face after the game's start. Only hair style, tattoos, and things like that. Anyone who wants a flatter face can start bashing their heads against a wall.