Horses were native to North America, and existed on the continent before humans arrived; they were probably wiped out by said humans. These 'giant ungulates' have much the same natural predators as bison and deer, which also happen to be 'giant ungulates', but whose presence I do not believe you would object to.
The "horses" you're talking about were a different species, they were much smaller, they disappeared 12,000 years ago, and their predators included Smilodon and dire wolves. Environmental conditions have changed since then. The feral horses I'm talking about descend from long-domesticated stock of Europe, Africa, and the Middle East. They are larger and more robust than typical deer. They inhabit desert country that currently doesn't have gray wolves and has only a tiny population of cougars. These two are really the only predators that could take down feral horses on a consistent basis, and they don't control feral horse populations in these areas. The vegetation in these areas is continually degraded by the presence of feral horses, which harms many actually wild species. Bison are not a factor because these areas are too hot and arid.
My objections to feral horses are not philosophical. If they occupied a sustainable niche in these environments I'd be happy. That just isn't the case. For more information about the mustang as it currently exists, I recommend the movie Unbranded, currently on Netflix. That movie sets up some sort of fake conflict between feral horses on BLM land vs private cattle on that land. It's true that horses' dentition means a single horse damages plants more than a single cow does. It's also true that neither domesticated animal should be present on much of this sensitive wild desert land in anything close to their current numbers.
Bison have the same issues with overpopulation and overgrazing, and they're being allowed to roam outside of Yellowstone again soon, which is making people nervous. They're destructive, dangerous, and carry diseases transmissible to other cattle, and they've been underculled in recent years, so no one is sure what's going to happen.
So you hear things where the people are the bad guys, but that doesn't make the problems for people living around these animal populations go away. It's a common oversight by people from (sub)urban areas; because they live in world built by and for humans, they forget they're only a relatively few miles in any direction from unforgiving wilderness.
The proper solution is to encourage hunting. The idea of "deer season" is crazy; they should be hunted continuously. To the extent that it is safe, this should be allowed in suburban neighborhoods and city parks.
I wouldn't be too concerned about horses when deer are already a much much bigger problem.
You did say it goes unpunished but having charges filed is a step forward.
Thus, almost nothing is ever done.
Hence, you see epidemics of prosecutorial misconduct, for example. Prosecutors go after people they know (or reasonably suspect) to be innocent, withholding exculpatory evidence, etc., just to score the credit of more convictions. Such people ruining the lives of innocent people are almost never (and I really that - it approaches zero) prosecuted themselves.
you mean invasive wild horses, don't you ? the ones that were brought here by western conquistadors ?
Which bureaucrat has gone to jail for making any decision of this sort? The BLM sold ~1700 protected wild horses to a slaughterhouse a few years ago, and I don't think anyone was even reprimanded.[1] EPA allowed 11 million litres of contaminated, toxic wastewater to pollute the a river, and no disciplinary action was taken (that I know of), even though it seems this would be negligence (or a criminal offense) if a private party had done it.[2]
[1] http://investigations.nbcnews.com/_news/2013/05/14/17708998-...
[2] https://en.wikipedia.org/wiki/2015_Gold_King_Mine_waste_wate...