At the end of 3.0 "The Eorzean Alliance is now whole with the inclusion of Ishgard. "let us defend eorzea from the Garlean Empire."
Since the emperor is at the front, seeing to the empire's efforts personally, whether its eorzean conquest or just an expedition to recover more powerful Allagan artifacts, i see the Alliance clashing with the Empire to prevent known but still buried war machines like omega-weapon from falling into the wrong hands.
Now that the Alliance is whole, after repelling the coming invasion, the Alliance will take on an offensive counter-attack to remove Garlean troops from the continent, what better way to start than liberating Ala-Mhigo?