If they were only going to pick ONE of these to key your custom character's story off of, would you prefer:
1. Your class.
2. Your race.
3. Your background.
Which one of those would you want the most to be the main determinant of what kind of storyline/origin they make for your character?
For me, it would be background. As I think you could do a lot more interesting things with like Charlatan, Urchin, Criminal, Acolyte, etc. than with the others.
I would keep it as it is right now or if I really had to pick one it would be race. Too many ways to go wrong with backgrounds, although if they could cover each of the billions of things players would come up with then I would agree with you.