No rancher who has been in business more than a few years is going to turn out more cattle than the land will support. That can be done by turning out 5000 head for two weeks twice a year or 500 for 10 months. Rounding up thin cattle to sell isn't the business ranchers are in. Maintaining the pastures to support a continued or growing AUM's is something every rancher knows or else is bankrupt very fast.
One of the big myths that the enviros have successfully promoted is that grazing permitees overgraze the land. The cattle industry in its ineptitude has done little to counter this lie. Calves have to come off the range in the fall with some pretty good gains to justify the grazing fees and all the indirect expenses associated with grazing permits.
As you said, hammering the land with more numbers than it can carry is the road to ruin for grazing permitees.