Even if we eradicated these dogs there would be a replacement, so we need to look at the whole picture of why this happens.
In an ideal world I'd like to see a licence required to own any dog. I say any dog because I want to see an end not only in attacks but also anti-social behaviour eg barking, and cruelty caused by ignorance. There are a huge number of well-meaning but seemingly clueless dog owners around it's staggering. To gain the licence you have to pass an exam on dog behaviour, including recognising danger signals, and dog training, dog care (eg the mental and physical requirements of different types of dogs), and expected costs of dog ownership.
I'd also like a ban on all dog breeding without a licence for similar reasons, and also to try and cut down on the thousands of poor dogs in rescue centres. To breed, one should pass an exam on genetic issues, bloodlines, etc. Before each litter you'd also have to justify why you want to breed that sire with that dam and prove it's in the best interests of the pups. You'd also need to prove you have a waiting list for the pups.
We also need to look at society, and address why certain types of people are drawn to certain breeds. Deal with the underlying causes of what drives the desire to have status dogs. Really look at the bigger picture and deal with the root causes.
Of course none of this will happen because it would be a huge undertaking, and it won't cure every problem, but unless we do it's akin to sticking plasters over a wound that needs stitching.