Think of it as population control.(somewhat tounge in cheek) Whitetail deer are the most hunted big game in North America. Their population is more than healty and always on the rise. Largemouth Bass are the most popular game fish. Plenty of them. Same with Canadian Geese, ducks, crows, etc... People that have hog problems can't kill enough of them. The state of Kansas has people that shoot scores of deer every year and just leave them lay. To protect crops.
We're lucky in this country to have an abundance of game animals, and non game animals. There are fewer hunters in this country than ever before for various reasons. So killing the occasional armadillo or 'possum is not going to cause the decline of the species. As long as the pest stay in the woods and out of the hen house, we'll get along great. Not trying to justify it...just saying.