That's psychotic obsession, not just trauma. Barbara values her life and avoids obsessing over the loss of her legs. She makes a point of it. (there was a great line about this in BLACKEST NIGHT, which by the way, along with this idea of Bruce, suggests to me why Johns doesn't like writing Batman--he's useless to Johns' style, which does not incline toward this romanticizing of emotional arrest)
One could also argue, okay fine, but WORLD'S GREATEST DETECTIVE. The idea being Gotham would have been deprived of that. Except that the point is always made that the kind of criminals you see in Gotham are a RESULT of Batman. Without him, you might not have seen them. The Joker, for one, whose becoming the Joker was Batman's fault.(at least in most versions of his origin) For that matter? NO Batman, no Joker. No Joker, no crippled Barbara.