Who's paying for vaccinating every dog? Who guarantees it was taken care of? Who makes sure its puppies are equally well cared for? Whose problem is it if it can't be found and does end up with a bad infection or disease and spreads it or ends up biting other animals or people?
Wherein we're back to the whole point of animal control in the first place, to make sure animals stay no threat to people.
paranoid much ?