This might interest you
https://www.cbsnews.com/news/samuel-...rcia-to-death/
That part of what you want is certainly already a thing. Picked a recent example from Texas sense you referenced it specifically but to my knowledge anywhere in America people are held responsible for damages caused by their animal on both civil and criminal levels.
One aspect of this conversation we have not touched is that it leans very hard towards the 'Nature' side of the 'Nature vs Nurture' argument. Carry that same parallel to people's races and it gets into some very racist territory. I personally believe both parts play a very substantial role but even more dogs are pack animals. They mirror their owners behavior the same as a wolf in a pack mirrors the behavior of their alpha. I feel like a very large contributing factor to so pitts having such high attack rates is that breed is often preferred by a specific kind of person. When I was in Ohio as a kid I even knew a guy that was giving his pit bull steroids.
You could draw the same parallel to any other breed specific behaviors. A dog with a huge drive to hunt is not an uncontrollable beast that runs down and attacks other animals. A responsible owner can spend the time to train it so it can be controlled so if some kid has a pet rabbit its not ripped apart in front of him.
We may just need to agree to disagree but I have trouble accepting the removal of an entire species of dogs. If we are going to start playing god with what species are allowed to exist I feel like we should start by removing mosquitos from existence.