Unless you are willing to throw poor people in prison over kittens, you can't really effectively enforce pet ownership laws, because the judgement-proof will keep pets.

I suppose you could have roving cat detector vans that would spay and neuter any cat they could get their hands on unless it had approved breeding chips embedded inside. I've heard a documentary on such a thing: https://www.youtube.com/watch?v=ZOonOtyoplY