I apologize for only taking the moment to read your first, but I'm not sure why a "See RdRdrFan response for my position" wasn't all that was necessary. I promise to do better in the future and save your comment for last.
I'll read his later and consider his points.
This explanation is exactly my point. No matter where you go, the common denominator of extreme animal populations is private property and how they prioritize management.
And extermination isn't the same as heavily reduced to a manageable population, I may have used them somewhat interchangeably but to your point, NM allows a few exotics to thrive within a certain core range where they fill an ecological niche and have relatively low competitive impact with native species. Then outside of that do a very effective job of keeping that population essentially crushed, with the odd band of animals turning up here and there.
And I'll admit fault for just generalizing landowners but I'm generally expecting some good will on the part of those I'm having a conversation with to know I'm not talking about the small guys stuck in between major population hubs (caused by landowners who see a value in keeping them around) and who truly want/need them gone (I'd wager not likely not the guys who own helicopters to offer hunts from, but I digress)
But allow me to propose a hypothetical. Say I pay a Texas outfitter $10k to shoot a giant Aoudad. So he drives me around, we find a canyon to check, and there he is...Aoudad of my dreams standing on the opposite wall surrounded by his giant harem of equals, younger males, and ewes.
If I were to get set up, then turn to him and say, "Hey, I hear these guys have a major negative impact on the environment and are super overpopulated. I know my hunt agreement said one mature male sheep, and popping one of those ewes should cost me $4k, but how set in stone is that really? What do you say I put a bullet into him, then you and I unload on as many as we can before they make it over the ridge? Won't cost you a dime, and we eradicate some pests."
He can do whatever he wants, it's his/his boss's land, but what would you honestly expect the response to be?
If it's anything other than "sure," and I knew they had petitioned for this rule in the name of necessary population control, I'm not going to get mad, complain, or lecture how unfair that is, but I absolutely have all of the ground to stand on to rib them about it a bit.