I am pretty split on hunting them for territory, which is what that really entails. Coyotes can kill cows, deer, and they commonly kill house dogs....but in most of the country they are not invasive. Unlike a feral hog, which is only there because Europeans brought pigs a few hundred years ago, a coyote was on all of our land a long time before we were. In many places they were only displaced by wolves, which make coyotes look like choir children.
In my state, there is an initiative to re-introduce wolves. My brother now lives in Montana, where I spend about one weekend a month, and I have seen what wolves around can do. Take a coyote, then add 50 pounds, more intelligence, better pack cooperation. They are worthy of a lot of respect.
I think that it is up to a rancher to keep them out as best they can through fencing, or do what they used to do and have sheepdogs out there to protect them. My neighbor has over 100 sheep on his property, and his 5 sheepdogs have meant zero predator deaths in the past 5 years....and this is a place with bears, coyotes, cougars, with property bordering a forest.
I understand the economic need to not have your cattle die. I just also think that it is incredibly arrogant to spread your cattle out over 100 acres, no real fencing outside of cattle wire, nothing to watch over them, and then get all grouchy when one of them gets eaten by something other than a human. I would not really have a problem with hunting them if they are on the property, after you have sustained losses, but I would have a problem with venturing into backcountry in the rough vicinity of my land, just to kill them indiscriminately....a hog is different for me. Thank god we don't have them here. Thank you bears.
"The soul that does not attempt flight; does not notice its chains."