Cutting grazing has helped wildlife. We have hunting ranches to prove that. And we have lots of land in the west Texas oilfields that haven’t been grazed since oil was discovered.
Well, if the ONLY goal is to maximize wildlife, then cutting all grazing makes some sense. However, I don’t believe in maximizing wildlife at all costs. The countryside I worked in around 1980, when grazing was higher, was still lush with wildlife.
Almost no humans besides ranchers and hunters ever go into many of these areas. Stock ponds, built to host cattle, provide steady water for other animals as well. Roads greatly improve access...good luck hiking very far into many large chunks of land in Arizona and Utah and Nevada. Without water - at 8lbs/gallon - you won’t last long.
I reject the idea that humans are evil, and using the land for forage and timber means we are abusing it. I will never be a preservationist.