Professional breeders are not the problem. It is not in breeders' interests to flood the market and collapse prices.

The problem is irresponsible pet owners who fail to neuter and spay their pets.

Santa Cruz County, California, where I used to live, enacted in 1995 a law requiring neutering and spaying of pets. (A breeder's licensed can be purchased for something like $100 annually, IIRC.) The numbers of animals in the shelters dropped dramatically.

Efforts to pass a similar bill at the state level failed, however.

I doubt it's an either-or situation.

However, I'll note that all shelter neuter and spay, so if it irresponsible pet owners who are responsible, than it is limited to those owners who did not get their dogs from a shelter.

Los Angeles is leading the charge on this. West Hollywood banned the sale of pets two years ago. Los Angeles city is doing so now.

http://www.examiner.com/article/los-angeles-poised-to-ban-sa...

The cost may still be a little too far out, but what about requiring breeders to register the dog's DNA sequence in some database. If the dog is found as a stray, a large fine is imposed on the breeder or the most recently registered owner. The fines could go towards programs for neutering and finding homes for strays. If particular breeders are frequently coming up as strays, they could loose their breeder license, etc. Of course to play my own devil's advocate, the risk here is that the owners who have lost interest in keeping a pet kill the animals instead of releasing them.

The point of this is not to make people adopt abandoned dogs because they can drive, it is to make people more likely to adopt abandon dogs by removing the conception that they are stupid/uncontrollable.

I think the real issue with overpopulating dogs is that they are treated as a commodity, so eccess stock is almost inevitable. Of course, every species that ever existed is always in a state of overpopulation, or exponential growth.