I hunt for fur. I don't trap much anymore but I ain't letting a smaller coyote go. If it has good fur it's getting killed. I use live traps for bobcats so that's easy if they're small they get returned to the wild or if it's a female it's a good practice to let them go.
Calling too, if I call in a kitten it's not getting shot. I'll wait until they're actually worth more.
As for deer and other things, someone's gotta manage their population. Hunters do a piss poor job of it. Sitting there all season waiting on a trophy buck and never pull the trigger on anything at all. No wonder I've killed more deer with a vehicle than a weapon. Deer ain't nothin but an oversized jackrabbit. Those cats and coyotes can eat all the little ones their heart desires. Personally, I'm not a big fan of deer. I don't hunt deer because you can't shoot 100 of em in a day. If you could I'd be all over it. The only good thing about a deer is the back straps or shooting coyotes over ones carcass.
From a fur harvesting standpoint letting certain things go makes sense. From a predator management standpoint, no so much. If managing coyote numbers is even realistic, it's not. If it were Jeremy would have already killed every coyote in his part of Oklahoma. That's not really how that all works.