Do you think if responsible breeders stopped breeding purebred puppies and everyone had a puppy from the local dogs home it would solve the situation? I think not.
Some people, not all, go to the local dogs home to get a cheap puppy/dog, the dog comes with health and insecurity problems, starts costing them lots of money, which they cant afford, and the dogs go back to face an insecure future.
Its the general public that need re educating on where they get their puppies from. Buy from a 'responsible' breeder, who carries out appropriate health testing for the breed, and ensures potential buyers know how to care for the breed. They will also take the puppy back should the owners circumstances change. The first step may be to put a stop to websites like epupz where BYB's can advertise their designer puppies and 'mistakes'. If they dont have an outlet to sell, they wouldnt breed.