As for letting nature take care of the prey animals, even if man were to stop hunting completely, I don't think that would ever happen. I take that back, that WOULD happen, but the outcome wouldn't be pretty. There are boom and bust cycles of Hares and Lynx, Fox and Lemmings, etc., without any intervention from man at all.
We have a very large ranch in west Texas that almost never gets hunted and I have seen the amazing boom and bust cycles you refer to. When the rains return whitetail and mule deer numbers go up. Also the rodent population explodes. Pack rats, prairie dogs, rabbits and hairs numbers skyrocket as do game birds like quail and dove. With that the predator numbers go up. Ground owls, hawks, Mexican eagles, coyotes, bobcat, cougar and rattle snake numbers increase.
And then the crash. The "black plague"(yes, that BP) hits the rodents reducing numbers by 80-90% off their highs. This affects the predators that starve or turn more of their attention to harder to catch prey like the deer.
I have witnessed this cycle going from very abundant(extreme) populations of animals to an almost barren landscape.
If we were able to intervene and control/flatten the swings up and down the animal population would benefit greatly.
