They have actually done some of that back in the days when there was trash packs in raids like split groups in alexander, or multiple times in 24 man raids. They also have the party split in Alphascape 4 right now, or 'soft' splits anytime there are two bosses in a fight that self destruct. Someone mentioned being thrown for a tank swap, while not exact, they did have the interesting byakko tank swap among others.
If you look throughout the game there are many examples of basically everything suggested in this thread, and more but usually as 1 offs, or a watered down version to 'test' it in a single instance. SE is a conservative JP company. Western games tend to just boldy strike out in new directions and see what happens, and that leads to a lot of variety and creativity. But it also leads to complete and abject failures that piss off everyone. Sure nax had all this great stuff, but what happened before and after? Instead of sticking to what worked they tried a buncha new shiz and re-made their game 7 times over. Playing it safer is just the mirror of the same double edged sword. Balance is in the middle, but thats a company culture question more than 'right' answer.