I can’t tell you how many cats i’ve trapped, spay/neutered and put back. I go looking for them and the cops tell me where to look too.
I don’t have a problem with that. It might even work, although I have reasonable doubts about how effective it is in the case of males. If you catch and fix 10 of a population of 11, all the queens in the area are still going to get serviced. Just going to be one busy tom!
Personally, I think vasectomizing the toms is a better move — especially if they are pure strays. They will still be effective in defending their territory and servicing their queens, but they will no longer breed litters.
BTW, I am very much a cat person, and have five of the furry little bosses in my apartment right now. All five are well adjusted and have their own little cat society. None of them ever go outdoors.