Yeah, definitely, shooting coyotes takes care of the problem better than anything else. I’m in the semi-city world, with pockets of high density housing developments, and even a few apartments, trailer parks, etc., but also a few horse farms within 5 miles of my house. I have seen a coyote or two, but took no action.
Yet...
Shooting one would be hard for me because they look too much like a dog. Let one get inside my fence and I’d probably get over it pretty fast.