It is a horrible situation, but I think killing them because they don't conform to our ideas of how pet cats or dogs behave is unethical. I have no easy solution, I wish I did. People should behave humanely with their pets, neutering when appropriate and not abandoning them. Keeping feral cats caged seems so cruel, so if I have to choose between a and b, I choose b. Some animals will survive. Ideally there would be capture, neuter, release programs, or some kind of birth control given in food like they can do with deer.
The vast majority of dogs and cats and other animals warehoused in shelters around this country are perfectly wonderful companion animals with no behavioral *issues* at all. That's not the point, not the reason they have no homes. The feral cats aren't kept caged - they go to the kill room immediately, if they end up at the pound/shelter - the vast majority die on the streets.
I think that every single cat and dog in this country should be neutered/spayed. I think that humans behave abominably to the companion animal species. Again, all of that is pretty much beside the point with respect to the question I posed to you, which question was posed in the context of grim reality, not in the context of a world where humans magically started behaving responsibly.
And in that grim reality, you currently have hundreds of thousands, perhaps millions, of pet cats currently warehoused in shelters, with no hope for a home, and a somewhat smaller, although still obscenely large, number of dogs likewise warehoused, with tens of thousands of additional animals coming into that system daily. What are you going to do - leave them warehoused for the rest of their lives, or set them loose on the streets, terrified, with little to no survival skills, to be preyed on by the humans who have already let them down so badly?
It's easy to say that its unethical to kill these healthy animals (and I never call it euthanasia). My point is that it's even less ethical to send them to long, lingering, fear and pain filled deaths on the streets.