I think all dog owners should need a license before owning one. This should trigger an inpsection, so dogs could be taken away from owners who are found not to be training them or keeping them well enough. The dog would probably be put down. Anyone caught with a dog, who doesn't have a license, would have dog put down and owner receives heavy fine. Anyone who's dog kills someone or puts them in hospital gets lifetime ban, and dog put down. I'd suggest some small identifier/badge to be worn by the dog on its collar so it's easier to enforce.
It sounds very harsh (and I am a dog lover) but there is such a blatant disregard for safety in the dog owning world, nothing is ever going to change without drastic measures. There must also be a massive deterrent for those who want to get a dog, but have no interest/skill in how to train it properly.
Me and my partner have a dog, and we'd have no problem displaying some form of ID on it's collar. We also don't take it to places where we think it will be unhappy or a danger to anything else. Even though he's 12, and small, and only ever licks strangers with their consent, it has to be one rule for all.