Breeding dogs isn't hard / has a low barrier to entry. You need a male and a female and a place to house the puppies. Conditions could be generally terrible. Enforcing licensing is unrealistic - who's going to do the inspections? Who's going to pay the inspectors?
Further, there are too many dogs and cats, period. Disincentivizing commercial breeding (making it harder to sell) is a _good_ thing, and rerouting some of the animals who would be killed by shelters who can no longer accomodate them is also a good thing.