I've got no particular "beef" with wild horses, but am curious as to why those who like to revile "invasive species" don't revile wild horses, invasive species themselves.
Actually the issue of the horse being an "invasive species" is more complex then it first appears. Horses show up prolifically in the fossil record in North America and Cortez' escaped horses which became the first wild herds, it can be argued, were actually a reintroduction of the species. The first horses that the Native Americans tamed were from these herds that predate the American westward expansion.