I refuse to have one because a horse is, as you said, dumb and they are fragile.
Here are the options for reducing the wild horse population.
Capturing and gelding 90% of the stallions. This will take a lot of time and money and it will only reduce the population over time.
Introduce predators such as wolves and mountain lions. Ever seem what a wolf pack can do? Not pretty. And then you will have the problem of what to do with the predators.
There is also hunting and leaving the meat to rot.
If you want to be truly cruel you can do nothing. Let the horses starve to death.
Or you can have small round ups and have the captured horses turned into hides and meat.
The last is the only logical solution.
“Introduce predators such as wolves and mountain lions.”
Nevada and most of the wild horse states already have extensive mountain lion population(s). Kalifornia has no mountain lion hunting, they are literally every in the state. The wild horse population has not gone down due to predators in Kalifornia. Mountain lions rarely attack healthy grown horses. Stupid idea. As for wolves, introducing wolves into Nevada will cause them to be exterminated on sight.
If $500 will get you a quality high-bred horse, nobody is going to waste time on 13-14 hh chance-bred little weeders.