The aggressive dog problem is essentially unsolvable.
There is clear evidence that some breeds (including pit bulls) are more predisposed to aggression than others. But many people simply refuse to accept this evidence. Researchers have only recently started to demonstrate that there are provable behavioural differences between breeds and many people still cling to the idea that those differences don't exist, and that a dog is a blank slate.
Any breed-specific rules run into trouble because it is difficult to establish a dog's breed, short of DNA testing. People clearly lie about their dogs' breeds when faced with these rules. A major part of the problem is indeed idiot owners, and they can switch to other breeds; anything big and nasty-looking will do. Hoping that the insurance market can deal with the problem runs into the same problem.
Switzerland tried a different approach: they mandated that dogs had to have obedience classes, and that owners had to take a how-to-train-a-dog class. This policy was discontinued just a couple of weeks ago, because it had no effect at all.
