Have you not played other Final Fantasy games? Completely anachronistic settings is how they roll. Most FF games from VII onwards have swords, modern-looking cars, traditional magic casting, and spaceships.

As far as Eorzea not being steamrolled, Solus didn't need to take over Eorzea to do the 7th calamity. The initial attempt resulted in the flagship of the entire empire being destroyed in its maiden voyage and then they gave up for a time until Nael triggered the calamity years later, which is all Solus needed anyway.

5 years after the calamity, Gaius sends his legion into Eorzea against orders, so it's not like they have the full force of the Empire behind them and Solus' plans work better when there's continuing chaos and primals being summoned anyway. If you pay attention to the story, the whole point of the Empire is to cause as much chaos as possible without actually stopping primal summoning and bringing the world under one peaceful banner like the mission statement is supposed to be. Solus' last act was to cause the Garlean Civil War, so now they're even more splintered and the IVth legion is left to their own devices.

The IVth legion hasn't been showing all their cards yet either. The storyline in Bozja keeps hitting us with the barely subtle fact that the Dalmascan and Nagxian forces won their battles too easily, which tells that the IVth legion is letting them win on purpose and something bad is going to happen.