It's definitely improbable for Eorzea to have been given so many miracles that saved it from Imperial conquest in so short a time (relatively speaking), but it's not implausible the way it's written, and that has to be enough.
Regardless of how improbable it is, the starting three city-states have to be available to all players at all times if for no other reason than because they're where seasonal events are based so all players (who've completed a modicum of the story) can access them. Circumstances will always conspire to keep them free, regardless of how plausible those circumstances may be. The writers' job on that front is to make those circumstances believable, and other than Midgardsormr saving Eorzea in a deus ex machina moment pre-1.0 I'd have to argue they've succeeded.
(Just like we already know Zenos' and Danny Boy's nefarious plan to cause the apocalypse isn't going to succeed for gameplay purposes; it's just a matter of what's going to happen in the course of their failure, and what victory is going to end up costing us. Gameplay demands will always mean pre-6.0 zones are completely, totally untouched by the Final Days, regardless of how plausible that may not be. Only a big, Calamity-level event could end up actually denying us access to sections of the world, and well, given XIV is in a good way right now, I just don't see that happenin'.)