Many coyotes live in isolated areas and they do what coyotes have done for millennia. I'm fine with leaving those animals alone. The ones that start hanging around farms and snatch and kill domestic animals are the ones I'm interested in.
They most likely belong to an overcrowded coyote population and removing a couple of them actually helps them. Like Art said, it's more like a chore, but, you can get some enjoyment out of the hunt. It can be challenging and exciting, even though they probably won't hurt the hunter, it still makes your heart race to have a predator headed straight for you.
Now, it's been said time and time again that everyone strives for a clean kill, that's the mark of a job well done, but if a bad shot occurs, feeling bad about it is normal. If you fail to sleep at night because of a bad shot, then hunting may not be the activity for you. Would I feel bad if I maimed a coyote? Absolutely. Would I lose a wink of shut eye about it? Not at all. Doesn't make someone a jerk, it's just a reality.
Not every bullet kills. Coyotes are not very sturdy for bullets, they die the quickest of any animal. You put a shot between any two of the four legs and they go down.