
It's worth noting that the lore book states that Eastern cultures developed completely independently until the Magitek revolution permitted travel across the previously impenetrable mountain range that separates Othard from Ilsabard. It's likely that "Eorzean" (officially "the common tongue of the Hyur") wasn't introduced in the East until that time.
Which is still a good few years ago, long enough that younger characters wouldn't remember a time before it - and longer ago than Doma's original annexation, certainly - but it's not exactly centuries ago.
Which is still a good few years ago, long enough that younger characters wouldn't remember a time before it - and longer ago than Doma's original annexation, certainly - but it's not exactly centuries ago.