Invasive cattle grazing on "worthless" land is a trope that's not true. Especially in the US west, we have seen massive ecological destruction at the hooves of cattle. They are not bison. They do not graze the same. The plants they consume do not regrow the same. They introduce a ton of issues.
Jon Muir called cattle, and other livestock, "Hooved Locusts", because of how they destroy the land.
The latest research is that we should absolutely be removing cattle from these "worthless" lands. We are still discovering how these lands work and we are finding so many benefits we had no idea existed.
We gimped nature and now we call that gimped version "how it's supposed to be". We use culture and heritage, "the western way of life", to perpetuate the systemic destruction.
But this trope of "white people decide the land is worthless" has a long history of being used to exploit the land/people for short term gain. Cattle grazing is a form of land theft. Destroying the land/ecosystem so people can't use it they way they have was, and still is, a form of land theft.
Also, the US west is getting so dry that cattle can't find enough grass so we do what? We pull water to grow grass in the desert so we can feed those cattle that are on "worthless land". Thereby making the issue worse. But are cattle ranchers and alfalfa farmers gonna give up their water? Ha! That's an affront to the Cowboy Way Of Life! We need cheap beef and stetson hats cuz this is Murica!