Banning mutant as an origin story, to prevent players from skimping on background, seems like begging the question to me.
Are you intending on forcing players to write a backstory, in spite of their inability or unwillingness to do so? A player who wants a backstory will create one, even if his power origin is "mutant", and a player who doesn't want to write one, will find a different low-effort origin to fill in the blanks with.
I personally find backstory to be a great part of most RPG characters, I'm just saying that this is kind of creating an in-character rule for an out-of-character problem. Engaging players directly to say they need a richer backstory seems like the better thing to do.