There is no 'subsidized public grazing'. There is Range.
Leased at far below the market rate. Compare private and public rates, and the costs to the federal government to administer these lands, and you see the subsidy.
https://www.blm.gov/programs/natural-resources/rangelands-and-grazing/livestock-grazingLIVESTOCK GRAZING ON PUBLIC LANDS
[...]
In Fiscal Year 2015, the BLM was allocated $79 million for its rangeland management program. Of that figure, the agency spent $36.2 million, or 46 percent, on livestock grazing administration. The other funds covered such activities as weed management, rangeland monitoring, planning, water development, vegetation restoration, and habitat improvement. In 2015, the BLM collected $14.5 million in grazing fees. The receipts from these annual fees, in accordance with legislative requirements, are shared with state and local governments.
Yeah, for every dollar collected in fees, $2.50 is spent...with taxpayers making up that ridiculous subsidy. Market value is far higher than what ranchers are charged. See
https://journals.uair.arizona.edu/index.php/jrm/article/viewFile/9843/9455 (Torell, L. A., N. R. Rimbey, L. W. Van Tassell, J. A. Tanaka, and E. T. Bartlett. 2003. "An evaluation of the federal grazing fee formula."
J. Range. Manage. 56: 577-584.)
Check out the vertical axes on this graph (from 2003...it's only gotten worse since then!):
While private land goes up, public land fees barely budge. Heck, in 2017, the fee was $1.87 per AUM (Animal Unit Month), and then in 2018 it's down to $1.41/AUM.
And yes, only Western states get this subsidy.