Complete genocide is unnecessary. The only ones that need to be killed are the tempered ones. If Ul'dah wasn't busy fighting Garleans, they'd march an army right into Zan'rak and clean house on them. The Garleans are the ones complicating matters by continually trying to take over the continent, forcing the city-states to waste resources on fighting them. Their offer to handle the beastmen problem for us "if we only kneel" is facepalm worthy. If they were really concerned about the beastmen, they'd let the Eorzean's sort it out and then move in to conquer the city-states when they are recovering.