But some FATEs should spawn once a week or once every few hours. Their rarity makes them special when they appear (please don't lynch me yet, just read on)...
...but they shouldn't be the target of farm quests like the Relic :|. What Squeenix really should have done for the books is just make it so you have to complete X FATEs in the area (maybe specific kinds of FATEs if they wanted to gate things by difficulty). Then behold, the low level zones are alive, I guess.

Alternately, let's not force people to do FATEs at all.