Coyotes have a lot to offer in a well balanced ecosystem. I would not classify them as pest. I think they get a lot more blame than they actually deserve. When you look at what feral cats, skunks, raccoons, bears, cougars, etc do to populations of game birds, small game, and ungulates. It is usually much more than the impact coyotes have. They serve an important purpose in keeping a lot of vermin in check.
I used to share many of the opinions that you guys have, but research, education, and observing the impact my hunting did around the ranches I hunted year round, changed my mind. The benefit to year round hunting in most instances, is observed around ranching operations. That is where you see the populations being backfilled by surrounding areas and the numbers can be kept in check. Individual coyotes that cause the most trouble can be identified and killed. And they develop a healthy respect for animals and humans.