As a matter of humane stray cat population control, cats are neutered and returned to their original territory. More info.
Successful results with TNR, a case study: https://www.mdpi.com/2076-2615/7/11/81/htm
Review of TNR as a means for population control: https://escholarship.org/uc/item/6z98577x
Ethics of TNR: https://www.frontiersin.org/articles/10.3389/fvets.2018.00341/full
Estimated to be more effective than neutering at controlling the population, are vasectomies and hysterectomies:
The original paper here: https://avmajournals.avma.org/doi/abs/10.2460/javma.243.4.502
Many that oppose TNR, are wildlife conservationists and birders, who produce research articles such as this one:
What the anti-TNR article fails to account for, is that there aren't sufficient homes for all strays, and that some feral strays cannot be tamed. This is overlooked with the motivation of protecting wildlife. TNR is a cost effective program at reducing stray population. Given there are not enough funds to house all strays in humane environments, the “correct” solution depends on which animals you choose to protect.
Conflict of Interest Statment: My cat was beaten to death by a female neighbor with bird feeding stations and a small dog. I always wondered why my cat stopped eating cat food, until later I realized, that he may have survived poisoned cat food. A year or so after his death, I was feeding a stray mom cat with a litter. I found the runt of the litter beheaded in front of my living room window.