I've thought about that, actually. In my epic fic, which takes place partly in Spira's future, the world eventually settled down thanks to a democratically-elected secular government made up of former leaders from all the factions and races and headquartered in Luca (since that's the closest thing Spira had to a neutral ground during the time of Yevon). The Youth League folded itself into the new government and became its military arm, the Spira Defense Force; New Yevon continued to exsist, but exerted very little influence outside Bevelle. There are a bunch of ways it could play out, of course, but this is the one I picked, and I think it works. :)

How about you? What do you think happens?