Originally Posted by
TheMightyMollusk
Flying from Doma to Eorzea would mean either flying over open ocean, or over Garlean territory. The former is implausible due to the time, distance, and need to let the birds rest; the latter is implausible because it's hostile territory occupied by the world's biggest airship fleet.
Also, remember that Hien was present for the final battle for Ala Mhigo. He and Yugiri could've teleported over. Of course, then we have to question how he got there that time, especially without anybody else knowing he was coming, just in time for a Big Damn Heroes moment, but that's just pure dramatic timing.