From the Georgia Department of Natural Resources web page concerning native* wildlife:
Georgia Law allows the taking of certain native species -- namely rats, mice, armadillos, coyotes, groundhogs, beaver, freshwater turtles, venomous snakes, frogs, spring lizards, fiddler crabs, freshwater crayfish, freshwater mussels, and nutria -- because of their status as a nuisance or other reason.
As mentioned above, armadillos are destructive. They are in the process of expanding their range in the US, displacing other species as they move in. Many areas, Georgia included, encourage hunters to shoot on sight. Farmers typically do not need encouragement as they are quite destructive. There are no initiatives of which I am aware to actually impede their spread, so to me this amounts to wonton killing of the animals.
* The nine-banded armadillo is a naturalized US citizen. It cannot easily cross wide bodies of water as it does not float. It does, however, know how to use a bridge even if it is prone to jump into the axle of a 4-by-4 passing above it.