I did some back-of-the-envelope math a while back that showed that if we wanted to make demand-of-pets match the supply-of-cats-and-dogs in the US, we'd basically each have to have one pet, at all times, for our entire lives. So, a family of four would need four pets. New baby: additional pet. Pet dies: get a new pet. One for each person at all times.

Barring that, if you want to minimize suffering of future stray cats/dogs (or limit environmental impact), it makes sense to do a one-time massive nationwide effort of scooping up all stray cats and dogs, and either spaying/neutering them, or culling them.