That would be a good idea. But there would still be the feckless who wouldn't care at jot.
That Bully owner in London, when his two dogs were shot by police was banned at the time for keeping dogs.
The English Bull Terrier that attacked my friend's two children {in a buggy and the toddler walking} was owned by a man who was also banned for keeping dogs {he had a dog fighting conviction}- but these two typical owners still went out and got aggressive dogs despite the dog owning ban.
A Bull breed RSPCA programme on TV {Now you tube} also showed irresponsible owners who had a ban keeping dogs also had Pits in grossly disgusting conditions, and the gobby owner was cussing and shouting and swearing- Par for the course.