To be more specific, the cows should take a bite and move on. This keeps the grass short, but doesn't kill it. With short grass, predators can see prey easier, so birds can eat and deposit droppings to add more nitrogen to the soil.
It's how most beef should be raised, though, IMO.
Unfortunately, if we were to take all the cows stuck in factory farms and turn them loose on BLM land, I somehow doubt there would be enough food out there for them.