They are releasing the cats again? - interesting. Not sure how to feel about that. Are you rural or city?
I'm in the city(Phoenix). It works out quite well. I have one that lives on my block, and my neighbor feeds it. It's not a threat to anyone, but it would be a nuisance if she kept having kittens (I caught her last litter and adopted them out). If you just get rid of them, another (probably fertile) cat moves into the territory, and they have larger litters in the absence of population pressure. Neuter cats are much less of a problem than fertile ones, too. There are a couple of fix-and-release charities around here which either do it for free, or charge a very minimal amount.
Same theory works with bugs, too. They release sterile ones, which keep the fertile bugs wasting energy trying to mate with them.