If you outlaw pit bulls, only outlaws will have pit bulls.
WTF is a "pit bull" anyway? Growing up we had a Staffordshire terrier (aka. an Amstaff), he was a big, powerful brute (80lbs), but the friendliest dog I've ever been around. However, everyone thought he was a "pit bull" and were terrified of him. Sure, he was protective of us, particularly my sister and I, but he never harmed anyone. In my early teens, my sister is a few years younger, he was often our babysitter until my mother came home from work.
The point is, a large group of dogs have been categorized as "pit bulls", when in fact only a couple breeds are known for having a potentially anxious temperament, meaning they need to be kept from small children, because kids can make unexpected sounds and movements that startle those dogs. Don't punish one just because people don't know how to properly handle the other.