What I am suggesting is to increase the meaning of Fate's, by increasing their threat to game play, increasing rewards and decreases the frequency of them. Meaning some, more rare Fate's may only come a few times a week.

I am imagining a boss like encounter with adds, rushing one of the quest hubs, killing npc's, players and rendering the teleportation crystal inactive. Quest givers are dying and all the sudden people might care more about joining up in a party or sticking it out for better rewards:materia or new crafting recipes.

Allow instances of the same Fate depending on how many people are in the area, that way more people can experience it with an appropriate amount of players. Once one fills up, spawn another and take those players out of the current instance.
The other could be a larger scale fate. Maybe the same fate is generated in multiple zones at the same time and the objective is for the server to complete it in each zone within a time frame.