Why do we keep wild horses captive? We've destroyed their natural habitats, and apparently now it seems like a great idea to hunt them. Wild horses would be far genetically healthier than purebred horses with increasingly less genetic diversity.
Well wild horses in this case are not a natural species. The wild horse went extinct in the Americas thousands of years ago. These are just the descendants of domestic escapees.
This. And modern horses are an entirely different species to those that lived in North America before. You might as well introduce zebras.