Suggestion: A Trashy Romance Novel Minigame/Questline
There is a longstanding tradition in several MMOs in which the game world has a famous writer of silly romance novels. Sometimes - such as in Guild Wars - you can meet these novelists or like WoW you can find their trashy books out in the world for a giggle.
One thing that Final Fantasy 14's story does not really feature but many people like to extrapolate is romantic interests between characters.
I'm honestly perfectly happy with the idea that the game never definitively states "X and Y" are together or that a particular character is or isn't interested in the Warrior of Light in some way. I think leaving such things up to the player's interpretation is the best route to take.
However, I do think there is an opportunity to capitalize on the desire for romance in Final Fantasy 14 without actually implementing it using that aforementioned method of the "Steamy romance novel".
My suggestion is this - imagine a side quest series where the Warrior of Light is called to help out an author of trashy romance novels to complete his work. Every single one of these books is the novelist's fanfiction pairing between some character from the game and the Warrior of Light.
The questline could involve a minigame where you have to play out the various dates and supply some of the dialogue or flirting in this fictional, tongue-in-cheek alternate reality - perhaps a match 3 or some clue-based quiz or the like. The success of the date (and novel) is thus based on the Warrior's performance.
There could also be some room for jokes like pairing the Warrior of Light with completely unlikely partners or the romance novelist asserting that their particular favorite is the only possible partner that would be worthy or sensible of the Warrior of Light.
I just think it would be a hilarious side quest opportunity and it could be fun to make a "dating mini-game" that is completely non-canon and tongue-in-cheek humor since actual romance options are out of the question.