My reasons are dependent upon where I am going after the yote.
If I'm after them "behind my place" its for protection of white tail and mule deer fawns. We got a dozen of them one year and the next couple of years each does raised ALL of their fawns to maturity.
If I'm after them out on the desert its for the shear sport of it.
Hides are worth little and cost to get tanned.
The meat doesn't seem too pleasing to eat. They have the wrong kind of muscle for good taste and texture. And the smell worse than a duck when cleaning them.
The single good thing I can think of about the coyote is that it, every once in a while, gets a cat.
Feral cats are another problem. We seem to have as many of them as we do yotes.