Here's another angle... the bigtime horse breeders. (Somebody mentioned what happens to the PMU colts and I think this goes along with it in its way.) We all know how pet breeders contribute to the overpopulation of dogs, for example. The horse breeders keep turning out a lot of animals, some higher priced than others, and are trying to make money selling those animals to either working ranch people, exhibitors (show ring types), or "weekend warrior" types. Then, the weekend warriors wind up with a high priced animal they don't know how to deal with, so for lack of enjoyment they wind up selling and often selling at a loss. Meanwhile, the breeders just keep on and keep on and keep on. So we have a surplus of horses whether they're grade (un-registered) or registered with any number of breed associations that run the prices up based on what the horse's parentage is. After a while, with so many horses on the market, the prices hit bottom and good horses go for little or nothing and many wind up with the killers. IIRC, that happened in the mid-to-late 1980's. The situation I just described happened between 1970 and 1985, so ya'll can see how people breeding anything to anything goes too because that was part of it too... folks thought "so what if I can't ride 'em; breed 'em" and they really hurt the horse industry.
As to mustangs not being indigenous, horses were indeginous but were on hiatus for a long time as was described. That's why the horse was new to the American Indian 400-500 years ago. Some of them thought the horse was just something else to eat. Others caught on, took up riding, and became the best light cavalry the world had ever known as well as being much more effective at hunting the buffalo. Now, my question is if some would be happier if the US Army had continued the program of killing off mustangs. If they had, some of us wouldn't know a world that includes mustangs, but wouldn't be happier for it. As for the mountain lions, I understand mustangs have a habit of avoiding areas they know to the cats to be in. Wolves? Re-introduce them and listen to the working ranchers in a chorus of wailing and gnashing of teeth for the loss of livestock and I don't blame them one bit on that part.