Not sure exactly what you're referring to unless it's their failure to regularly round up and ship a bunch of the horses off to the glue factory. They're pretty, but they're essentially hoofed vermin that drive out other large herbivores and with the last couple wet springs we've had I'm worried they'll be starving to death all over the place pretty soon.
Like cattle? Hardly indigenous either, and ruin vast tracts of land by overgrazing. So do sheep. They are far more responsible for ruining prairie ecosystems than horses. It's obvious profits come first, so other species have to go. The BLM holds helicopter roundups, which are cruel. It terrifies the animals and young foals can't keep up, get separated from their mares, etc. Why can't wild horse stallions be gelded to control numbers? I think the BLM has long been headed by absolutely incompetent people, or they would have had a decent non-lethal plan in place for the past few decades.