License for owning pets?

It is easy to enforce.
For example -
Have all pet stores, local, chain, or online require people to show the license proof before making an order. It is as simple as to show your ID when buying booze. For ordering online, simple add one blank to fill your license number.

It also requires to show license registration at the vet. It is also easy to do.

For dogs, cats, and birds, a simple requirement to have a tag with license registration number on them would not only be easy, but it also would be good for tracking down lost pets.