But they aren't wildlife at all. They're feral domestic horses, absolutely not native to the land they roam.
It is a problem because there are more than the land can support. Yet on the flip side, the annual round-ups aren't exactly humane. I think they should do a lot more population control, try to sterilize them if at all feasible (and that would be a very difficult thing to do, I realize), and over time try to elminate them from the lands and place them in homes where they will be trained and used, just like any other horse. Beats starving or being shot.