I know quite a few guys who like to hunt coyotes and prairie dogs because they can. These are not people who are concerned about predation on livestock, nor on prairie dog holes breaking a horse's leg. They are just guys who like shooting the critters, and who can do so at will because those animals are considered fair game where they live (due to damage to livestock).
I don't know anybody who eats coyote or prairie dog.
A lot of guys kill wild hogs whenever possible. The meat does get used on those, in general. Again, those animals are considered fair game in many places because they damage crops. Yet, most of the guys I know who hunt hogs are not farmers - they are guys who like to hunt.
My point again being, don't make this a moral issue about the evil feral cats. If you place a value on the animals they kill, and if feral cats are legal prey where you live, then have fun. But a lot of humans behave in much the same way as those cats do.