HOW do you stop it? If you've got some ideas, I, for one, would be happy to hear them.
Even AKC purebred breeders haven't managed to stop the irresponsible puppy mills and BYB of many popular dog breeds.
Education is one way, and the growth of the Internet has helped increase awareness, but it's slow. It takes time for people to assimilate information, and pass it on. Eventually that may make a difference, but in the meantime, you can look in the newspaper ads of anytown and probably find "wolf hybrids" for sale (as well as almost any breed of dog).
How many people who get dogs actually do ANY research before they bring home that puppy? Look on the rec.pets. newsgroups and any number of other places and they're filled with people needing help &/or complaining.
You can try to force legislation on people. Although I support responsible owner laws, I cannot and will not support any kind of breed (or type) specific legislation, for a number of reasons. What other choices are there?
So, meanwhile, quite a few of us spend considerable time, one way or another, trying to help people learn and deal with problems that arise, on and offline.