The probably with this question is that you have to keep the populations low. If they get out of control, the entire population suffers from lack of food and space, etc. So, just like with deer, fish, and any other wild animal, the populations have to be controlled so that the entire ecosystem does not suffer. This is especially true because wild horses in the US are just decedents of domesticated horses brought over by the spanish in the mid fifteen hundreds and sixteen hundreds. We have the responsibility to take care of this.
The means of this control is the debate. Do we shoot the horses like we do deer? Not likely because we don't see horses as a source of food. Humans as a species is too connected to horses to do such a thing (I personally could never do it). Therefore, we have to take the individuals out of the population--rounding up. This is a problem too because what do you do with the horses? Though horses themselves can be cheap to buy, they are not cheap to maintain. Therefore, not every horse, probably not even half will be sold. That's where wild horses are put down and used for whatever purpose (like their meat being used in dog food, for instance).
I think it is important to control the horse populations because their overpopulation can effect not just them, but the other animals in the ecosystem as well. However, we need to find a solution to the problem of what to do with the horses once they are removed from their herd. Can we relocate them into a new herd? Make adaption free or help out with the first years of owning one? There isn't just the animals to take care of, but the economics--making affordability, etc--the affects the horses can have on different communities if they are relocated. There's just a lot of problems with the whole ordeal. It's not even really anyone's fault. It's just a mess.
This is my opinion really, and I'm not just bsing it either. These are the same kind of issues people have had to consider with plenty of wild animals. It's just far more complicated because it's horses. Like I said, not many people are willing to eat them like they are deer.