Statements like that are misleading and incomplete.
Truth is, public lands in the western U.S. can only support that many wild horses and burros because they’ve been consigned to ‘other mandated uses,’ such as the grazing of privately owned cattle and sheep.
Section 3 in the Original WHB Act, which calls for a ‘thriving natural ecological balance’ on public lands, orders the Secretaries of Interior and Agriculture to confer with state agencies to ensure that wildlife have access to sufficient resources and are not squeezed out by the horses and burros, especially endangered species.
“All management activities shall be at the minimal feasible level and shall be carried out in consultation with the wildlife agency of the State wherein such lands are located in order to protect the natural ecological balance of all wildlife species which inhabit such lands, particularly endangered wildlife species.”
There is no provision for domestic livestock! (That’s one of the ‘errors’ in the WHB Act that the public-lands ranchers and their political allies, mostly Democrats, ‘corrected’ when they drafted FLPMA.)
Statements about roundups and other actions, that they are required by the WHB Act of 1971, are also misleading. That statute is gone, destroyed by the ranchers.
Off-range corrals and long-term pastures are flooded with (former) wild horses and burros as a consequence.
Current herd management practices are justified by the WHB Act of 1976/1978/2004.