No, not a ranch, but I've seen the destruction of public lands from over-grazing out West.
I have seen land in National Parks stripped by buffalo who retire to private pasture to graze. I have seen land which might support one cow/calf unit per 10 acres with stringy mustangs trying to eke out a living==but no cattle. But most of the rough land I have seen was denuded not by overgrazing but the indigenous fauna. Some of it is just not conducive to growing much of anything--soil type, mineral content, lack of water, etc.. not grazing, just geology.
Where are you getting your information?