The same reason inbreeding any mammal is eventually disastrous. If inbred in the wild they go extinct,if inbred in captivity they become retarded. New bloodlines with the right characteristics breed better mammals.
“...inbred in captivity they become retarded...” Did you find that in the Funk and Wagnell under ‘liberals’? :-)
There is no reason to save wild horses for breeding stock there are plenty of captive ones around to never worry about inter breeding.