Just stop. Stop bickering about cats being the problem. The problem is humans... We are the problem. Their existence is due to us. Their domestication is due to us.
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.