According to 43 CFR 4710.1, a federal regulation, management activities affecting wild horses and burros shall be in accordance with approved land use plans.
This is government writing its own rules, perhaps at the behest of special interests.
It’s not necessarily a bad idea. You don’t want to place 1,600 wild horses in an area that can only support 1,200.
Unfortunately, there is no requirement that the plans assign most of the resources to wild horses, which explains what you see today in many wild horse areas.
Now that the link to the statute is broken, you’ll find 200 wild horses in an area that can support 1,200, accompanied by hundreds or thousands of privately owned livestock.
The advocates, unfazed by the practice, worry instead about the best way to get rid of ‘excess’ animals, horse #201 and so on.