It depends - if the person I know who sells hides is available, I have a source to send the animals through. If I am otherwise doing some other form of hunting (usually deer hunting when I see the most coyotes), I leave them laying. Good-quality coyote pelts around here are not very common - too many dogs running around and the coyotes get pretty mange infested. I am hoping to get a good one (either a mature one with a great coat, or a black one (have shot one - couldn’t find it for a few days) to get mounted or at least tanned.
Coyotes kill livestock, pets, keep the turkey’s from having successful hatches, kill young deer, and actually have been known to be aggressive towards humans. They are primarily considered a pest. At times past, there have been bounties on them - you turned in tails to collect.