History would take exception with your statement. The mass deer starvations on the Kaibab Plateau in the early part of the 20th century along with the deer overpopulation problems at Yellowstone earlier than that were in part due to overcontrol of deer predators such as wolves, mountain lions and the like.
"Playing God in Yellowstone" by Alston Chase goes into a very detailed review of how the deer population was impacted by well-meaning folks who depending on the era made poor predator control decisions that resulted in deer populations rapidly expanding, irrupting and then rapidly declining.
You pick two examples and I specifically said wolves, not cougars, bears or coyotes, the Kaibab Plateau is not an argument for the preservation or introduction of wolves now.
National parks such as Yellowstone are a poor example arguing for the introduction and need for wolves. With Game Depts that manage deer and other game populations through legal hunting outside national parks, especially in the Western states its been shown wolves are not needed. They’re destructive of game animals that are legally hunted and destructive of livestock, not to mention the threat to humans if their numbers get too high.