While I love the FATE system, I and many other players have found that it causes a great deal of interference sometimes during leves or other activities to those who don't intend to take part in the FATE. Many times now I've had a FATE start on top of a leve I have going, I find myself immediately inundated in monsters from both my leve and the FATE at the same time, and my HP hits 0 before I can think fast enough to save myself.
I know that with FATE chasing becoming a popular leveling method and means to obtain Grand Company seals, the time period between when a FATE begins and ends is getting shorter and shorter, so implementing some kind of "join" or "decline" system might be a bit too time consuming for some players. Perhaps a priority setting that would allow your leves and quests to take precedence over a FATE, keeping the player out of the fray unless the player chooses to take part, or simply attacks a monster that is part of the active FATE.
Just some thoughts.