FATE parties are a relic of the launch month, when people found out that grinding (or rather, zerging) FATEs were actually better EXP than leveling through the main quest and side quests. During that time, solo FATE grinding was not viable because FATEs end so fast, you'd get at best a bronze and very little EXP.

In the current state, there's no reason to require a party to grind FATEs, although I suspect that for a solo grinder it's better to move to different zones after a while to avoid the FATEs scaling up.