Yes, but then you would also have a bigger black market for animals too. Ergo, more puppy mills. The main reason, at least in the U.S., that drivers licenses reduce accidents, is that there are various ways you can be caught, be arrested, and there can be jail time involved. Once again how are you going to enforce such a regulation? Stop people at petsmart buying food? Stop everyone you see with an animal? Force them to present a license to get veterinary care? And are you actually going to punish people? It really makes very little sense, practically speaking. It will either cost more to administrate than the licensing fees will ever cover, or it will just be a farce.
