As someone with zero interest whatsoever in animal breeding, this kind of restriction seems way too draconian and incompatible with a free society. I'd rather have there be too many stray animals forever than for that to be implemented.
(I’m not advocating for a ban but there aren’t any good options here. )
How can a breeder, who is incentivized to create a stream of puppies to sell, be compatible with a society that is trying to reduce euthanasia for animals? Breeders already have to deal with puppies and kitties "aging out" of profitability, an organization like this just subsidizes their cost of dumping unwanted stock.