The .17 HMR is one fine little round - for it's intended purpose. I love the cartridge. It's as good a light-weight crow sniper as you can get, in my opinion. It's adequate on groundhogs with good shots. No doubt it will kill fox, bobcats and coyotes too, but does that mean that we "go after" them with that tiny round?
A lot of guys on here have proved the HMR works for predators, but also a .22 long rifle has killed many head of deer, as well as some rather large barn yard hogs that I watched my Dad shoot in the head. That doesn't necessarily mean those tiny rounds are ones of choice for the job at hand, although they have proven capable of downing an animal. Would you deliberately go after a grizzly with a .243?
Better to pick a cartridge with reliable power for the specific job.
Just me thinking out loud, and that's not to put down anyone who uses an HMR for such things with success. If that's all I had to hunt coyotes with, or was restricted to it, I would do it, but do it carefully. I just don't like to see wounded game run off, whether shot with an HMR, 6X45 or a 7mm magnum.