Coyotes predate livestock, especially the smaller species such as sheep and fowl. I will do my part to keep the prices of meat down. Crows can strip a vegetable garden in minutes; they also can decimate a pecan crop over a growing season.
So, in effect, they are vermin. Don't get hung up on eating what you shoot. That is a red herring tactic used by anti-hunters. There are several reasons for hunting, and food is only one of them. Some others that come to mind are disease control, domicile preservation, and physical safety.
You can eat crow, and I have on occasion.
Coyote fur is superb for clothing.