Ok, not taking the time to dig as deep or as reliably. But, looks like the US has 305 million AUMs worth of grazing and BLM leases about 10.8 million AUMs and the USFS about 5.5 million AUMs.
So, 5.3% of US grazing AUMs help produce 2-6% of cattle.
Of course, we I don't know the breakdown for AUM use as clearly not all are used for cattle (public or private).
I guess the question comes down to should tax payers subsidize industries so they can exist in locations a free market will not support? And, the answer to that is 'it depends '.