First, let me turn it back to you. What are you going to do when the thugs switch to any one of the other few dozen breeds of large, aggressive dogs because you’ve banned pit bulls? When more people get hurt, because some of those breeds ARE people-aggressive, unlike most pits? And then you ban that breed, and they switch again. And again. And again.
People will always be able to find or breed large and aggressive dogs. How far are you willing to go? Ban all dogs? Ban all dogs over 5 pounds? 10 pounds? 20 pounds? No Labs, no Collies, no Goldens, no Huskies, no Shepherds, no birddogs, no Boxers, no Bassets, no SharPeis, no Aussies, no Bulldogs, no Corgis, no Terriers to speak of…how far do you go?
Are you aware of the history of breed-bans? Do you realize that the “most dangerous breed EVAR!!1111!!!” changes about every decade or so?
Now to answer your question - it’s called law enforcement. If we have the time and money to go around finding, impounding, and killing supposed pit bulls (because many are not really pits), why can’t that time and effort be spent instead enforcing the leash laws, licensing laws, etc.?
Change the licensing laws so that pets MUST be fixed unless you’re a registered breeder - and make it extremely difficult to be listed as a registered breeder. (IMNSHO, the AKC has a huge responsibility for the puppy mills and backyard breeders and should be collectively bitch-slapped, but that’s another rant entirely.)
Up the fines for off-lead dogs, unlicensed dogs, etc. Include loss of all animals for repeat offenders and then don’t let them license more. Make it PAINFUL for people to ignore these laws - and then enforce them!
Hell, require dogs to pass obedience classes by a certain age to maintain the license. That will help at least some people, who are ignorant rather than intentionally idiotic. Obedience classes are about training the owners not the dogs anyway, so at least a few more people would get their animals under control.
Put some teeth into animal cruelty and neglect laws and enforce those.
Yeah, you’ll still get the idjits out in the country who won’t be affected by any city ordinances (although I think most cruelty/neglect laws are state level), but y’know what? Most rural folks around here have guns. If that Lab I mentioned above had been around when I lived in the boonies, it would have been dead long before it bit someone.