This the best thing for truly feral cats.
And remember that, when you kill a feral cat, she may have a litter of kittens who will starve without her. (Or be eaten by other animals). Better to trap them, & spay/neuter or humanely put down.
The most likely reason for a decrease in small wildlife in a rural area is NOT feral cats; it is
coyotes. (No, you don’t always see them. In fact its rare that you do).
I understand your frustration, but unless the cat is a danger to you, your family, and/or the family pets, I think it is wrong to shoot them. (I know it is illegal, an ethical concern in & of itself).
Mind you, if a feral one were menacing
my cat, I know what I would do…One more reason I keep her strictly in the house!
But the humane society will kill the cat
painlessly. It will simply go to sleep & not wake up. Being shot is NOT a good way to go. (Trust me: I have dressed bullet wounds.)
Most feral cats reproduce because no one has taken the responsibility for having unwanted animals put down peacefully. They don’t want to pay, so they

dump animals out in the country to starve. That is really immoral…Especially since the truth is, that every humane society I know of, will ask for a donation for spay/neuter of animals. The amount is nominal, not what you would pay a private vet. (Who is probably the one doing the surgery for the organization.
I also want to point out that, studies have been done by humane groups here & abroad, where the stomach contents of feral cats who have been put down are analyzed, and cats very rarely have been found to have eaten birds. Even squirrels are rare. The most common food items found are: insects; field mice; rats; & parts of other pests like woodchucks.
I have had cats all my life, & lived around cat owners–hundreds of cats, & I have only known of
two in the entire lot who have killed birds. In both cases the most common bird killed is the barn swallow. If you have never had these guys bombard you, you are lucky. (I have gotten so fed up with them, I have killed the stupid birds myself, not waited for a cat). They are a menace, & what makes them a menace makes them prey for cats…
(I did once have a poodle who

delighted in killing robins. But we are talking cats).