It wouldn't cost billions, unless we listen to people who keep acting like these are people. If we have to have little funerals or something maybe. Maybe it makes me a "nazi", but I could come up with a few "final solutions" for pit bulls that wouldn't cost much at all.
People ruin the rights of others.
For instance, I'm not picky about what kind of barnyard animals my neighbors want to own. There will always be that guy, though, that doesn't care for them, lets them roam the neighborhood, lets them destroy other people's property, etc.
So, no one can own livestock in most suburban areas. Does that mean that to protect our right to own barnyard animals we have to let that idiot ruin our grass? Evidently, because even if he has to clean up his mess, the time and effort and trouble is still imposed on us. Sadly, it is easier just not to allow it at all.
People who own dangerous dogs screw things up for people who want to own reasonable animals. Is it testosterone or some kind of hippie "animal spirit" thing that makes people so die-hard about owning a particular breed of canine?