It would be nice indeed. But if we're gonna get that crazy why not allow character rebuild but you must keep your race the same?
I was very disappointed to see my char after the fun little character animation. He didn't look anything like what I expected but I just didn't want to spend all day seeing every Elvaan to see how I felt about them all. Or maybe I just wanna change the hair color...

wait... start with hat toggle, please. I would love to hide the 'flying diaper' on my BLU