Licensing issues aside, my issue with an Olympics type event is about who competes and who the teams are.
The teams would have to be the Grand Companies.
If the players are competing, then I think we need mini-game like events .. so maybe after Gold Saucer is added. Also the games would only be available to players registered with a GC.
If the players aren't competing and just facilitating organizing the games and we get cut scenes with the GCs competing .. that could work but seems less fun.