Before I say this, I feel it’s important to clarify that I have nothing against any individual dogs or breeds, and I don’t think any animals should have to be euthanized unless they’ve shown that they as an individual are dangerous.
That being said, I can’t think of a single breed besides border collies that has any valid reason to exist for another generation. If breeders were more worried about breeding for health instead of looks and behaviour, I might be okay with it, but I’ve seen too many pure bred dogs with debilitating health defects due to their breed. German Shepherds are beautiful dogs, but it isn’t worth making them suffer through hip displasia just to look at them.
I obviously don’t think every dog except for border collies should go extinct within the next 20 years, but a law that criminalizes breeding wouldn’t stop all dogs from breeding. There will never be a shortage of dogs for people to adopt, and a mutt is just as good, if not better, than a pure breed.