I think I understand where you're getting at. If you think of them as "actors", then yes they have the potential of playing any role regardless of what settings they are in. Such as how "humans" are acceptable to appear in many multiple cultural roles. You don't see them as one of the many human cultures and societies... but more as whatever culture it is tied to.
However, these unique races are designed to fit a particular cultural role. Such that they have been pretty much "type-casted" to fit a role for that particular FF universe. They are strongly identify with the role it plays.
Such as when I think viera I think of three things; mist frenzy, attuned to nature, and reclusive society. Now I think the former two might conflict with how FFXIV universe is designed. You can't have a viera going into a frenzy every time it walks up to an aetheryte, you can't have a viera attuned to nature without being a conjurer naturally. (Granted that not all vieras were magic users, but they all had the innate ability to be one. Which is why in the FFTA games they were the only summoners, elementalist and can access other mage type jobs)
Eventually I might be able to forget what a viera was after aggressive re-branding, but even now I'm still having trouble not seeing a roegadyn as a galka. (well this could also be because there's very little cultural background references for races in game)