Another reason for doing FATEs in Stormblood to level is the new bonus exp system added for FATEs in SB areas - random FATEs will have a 'bonus exp' modifier on it, in addition to the 'Twist of Fate' effect, in that there is a chance of an enemy spawning during a FATE in SB areas called a 'forlorn maiden' (it looks like a crystal fairy) that does not seem to fight back. Destroying this before the FATE ends will then grant you the 'Twist of FATE' status that is a buff to the exp gained in the next FATE you do (which stacks on the aforementioned FATE bonus exp on top of that), although the effect wears off after that next FATE is completed, there is no limit to how many times you can get it.

So exp tends to flow in with FATEs in SB without even trying, to the point you will probably end up overlevelling easily in the main scenario, not necessarily a bad thing.