The only people who still do FATEs are those who afk bot in N. Thanalan. And levelling battle classes with Leves is the worst idea. JEFG > Queue for the highest level dungeon on the list. Do Low-level/guildhest roulette once a day. Do your hunting log, soloing any FATEs you run into on the way. FC buff + food help too.

Seriously if you think this is a grind, you should have tried levelling in XI pre-Abyssea.