It’s also true that BLM can and does change the terms of the grazing agreements unilaterally, to which the ranchers have the choice of “take it or leave it”. No one could operate a business under those conditions.
Actually Congress does that, and the agency administers.
Congress passed the Taylor Grazing Act and created the Grazing Division to administer it. They weren't very successful so they changed the name to US Grazing Service and relocated to Salt Lake City.
Then the US Grazing Service was merged with the General Land Office to create BLM.
Then Congress passed FPLMA in 1976 and BLM's mission was changed to Multi-use and tightening control over the lands. The Land Office duties were shifted elsewhere. Homesteading ended at that time.
Congress enacted numerous acts back in the 70s to deal with problems beside over-grazing: OSHA, MHSA, Endangered Species act, Pollution control acts and creating EPA, Logging policies to deal with clearcutting, the Magnussen Act to regulate the ocean fisheries.