If you leave them in the wild, they don’t die of mismanagement, they die of starvation, vehicle collisions, disease, etc.
There were wild horses in NA, but they were driven to extinction by indigenous Americans. The ecosystem is fucked up in North America because most of its mega fauna and almost all of its large predators were killed. Wildlife managers are trying to do the best they can with the situation they inherited. I’d love to be able to bring back the dire wolves and cheetahs, and lions, but we can’t yet, so humane euthanasia may be necessary.