What, being ineffective? Can happen a lot of ways. You can be fairly effective without very good stats, for that matter. For instance if you make her a wizard and she gets mad and starts throwing magic missile, her stats make no difference. Neither does the choice of magic missile define her in that instance, since she could just prep something else tomorrow. OTOH, if she's a Sorcerer, the fact that MM is one of her spells is a little bit defining.
But, are you seriously trying to assert that /what/ a character can do can't be character defining, just because RP can be? Or are you arguing against the idea that /only/ capabilities are character-defining?