Yoshi has talked about this before and it's not possible as the ratings board would likely consider it gambling and it would affect the games rating. I believe this was talked about at either a live letter or one of the fanfests, but I can't find it right now. The only thing I can find is from an official blog post regarding mahjong:
https://na.finalfantasyxiv.com/blog/002618.html
""Can you guys see if we can put mahjong in FFXIV?"
Those were his words! FFXIV and... mahjong? Well, this was a request from the director and producer himself, so naturally the dev. team began to look into it.
It required a bit of extensive investigation though, as FFXIV is a global game and regulations differ across regions.
Sure, it may seem like a harmless addition, but different countries and cultures have different perceptions on games that could be considered "gambling". This is why Yoshi-P's original idea to implement poker in FFXIV hasn't come to fruition yet, but he's thinking about putting it in one way or another...
When we found that we could indeed add mahjong to the game without legal or rating concerns, the UI team got very excited - "We'll do it!", they shouted. (Or so Project Manager U tells us!)