Should the law restrict what animals can be kept as pets?

The thing that concerns me about this, is that we can't make laws to control the movements and doings of every person, and often the laws make things worse, rather than helping. People will find ways around the law if it exists; or just do something illegally. The only people it does affect are the ones who are already obeying the laws.
For instance; many places have restrictions about how many dogs you are allowed to have. Here, it is 3 dogs.
If someone is a good dog owner and has 4 dogs, is that terrible ?

On the other hand; the people who are raising pitbulls for fighting are still doing that, just doing it somewhere that is not as obvious as having them running around in their front yard.
So, all this law does is stop someone who might adopt and animal from the dog pound and save its life, and doesn't stop the lawbreakers from abusing their animals at all.