Apparently predators are necessary to keep the natural balance and control the grazers. Many years ago, a friend of mine was a game warden in Michigan, and he told me the predators had been wiped out, thus ruining the natural control of the deer population. The result, the deer population exploded and there was not enough available food in the winter to support the unnaturally high population and the deer would drop dead before his eyes due to starvation.
The moral of the story seems to be "predators" get a bad rap, and because they are evil predators, killing them for no reason other than killing them is ok. Kinda lame.
Another friend of mine father owned a place down here years ago called the Aquatarium, a sister to the Miami Sea Aquarium tourist attraction. Dolphin shows, huge aquarium with a myriad of sea life. There was a conservation component to the place, but still a tourist deal with the dolphin shows the main attraction.
When the tourism industry began to change, and more zoo type places seemed to be the rage, the Aquatarium, added displays of some of the big cats. While the cats were in larger containment areas than had typically been found earlier in the 20th century, ultimately it was not sufficient with places like Busch Gardens providing "natural" habitat for most of the animals, animals of all kinds. The Aquatarium had had its time and was torn down to build condos.
The point for me is, after spending time with the big cats, and particularly two young black panther cubs, it is beyond me that anyone could shoot a big cat. IF, and that is a big IF, it was somehow a threat or had been proven to have injured or killed someone, then it is understandable. Even then, you are in their world, and caution should be used at all times. Once you see them in the wild, it is unfathomable to me to shoot them. There are so few of them left in the wild, it is a shame some folks get off on killing them.
In my world, I spend a lot of time on and in the ocean. We "hunt", but use fishing poles. We also spear fish. Never take more than we can eat, and don't kill what we don't.
I dive and surf with sharks in the water. That is simply the way it is. Florida is the shark attack capital of the world. Guys get bit every year, with a fatality very, very rare. I know there is a risk, but I choose to take the risk. What I don't do is kill sharks because they a "predators". If I was threatened and believed I was in imminent danger, say spear fishing, of course it would be considered but unlikely I could kill one but could ward off an attack. I do always remember tho I am in their world and don't knowingly push the limits or look for trouble.
So, I am trying to wrap my head around the concepts that it is ok to kill a predator for what seems to be no real reason other than some perceived threat that the hunters put themselves in.
FYI - i did some searching on wolf populations in the US. Many have been reintroduced into areas after being wiped out. Part of the reason was to maintain the balance as previously mentioned. That being said, the wolf population in mainland US is nil. In 2016 Michigan had a population of 618. Wisconsin 866. Oregon 77. Washington 48. New Mexico Arizona had a combined "experimental" population of 113. Doesn't appear that wolves are huffing and puffin and blowing that house down. So the story that wolves are the cause for the major decline in elk populations doesn't seem to hold water. A myth. It is more likely, that since predators have been wiped out, and over breeding relative to the human encroachment on habitat , the remaining habitat cannot not support the population.
Here is a link to an article that addresses your statement and corrects the record.
https://www.outdoorlife.com/blogs/newshound/2013/06/study-wolves-not-cause-wyoming-elk-decline/Oddly enough, a couple of articles address hunting as a cause for the herd population decline.