Whatever the law you always get people who ignore it, but it does help to maintain some sort of order in our society. Ok most drivers speed at some time or other, but generally speaking they stick to the rules - or at least a bit above them. With no speeding laws at all, it would be a free for all.
At the moment we have a free for all for dogs, albeit that there are stiffer penalties for people who let their dogs maul livestock. I do think if we had licences and strict liability for owners if their dogs injure someone it would reduce incidents.
Also stop foreign rescues coming in - they are not "rescues" they are bred in puppy farms for gullible Brits.