In the dog/restaurant analogy -

You probably would not have any standing to sue the restaurant or the government, as the laws prohibiting dogs are for health reasons, not safety reasons.

Also, what if your dog incited the other dog to attack - now you are the one getting sued by both the restaurant and the other dog owner - oops, not too much protection there.

You would have a course of action against the dog owner who failed to control his animal - said animal having bitten you.