So I keep receiving quests from the story or Grand Company or GC leves, and any number of related situations where I HAVE to, that is, I'm REQUIRED to DROP MY PARTY just to execute the quest. It's annoying for all concerned.

Often times, this is a situation in which the player is tasked to work with other npc members during an important battle or situation.

All I have to say is this... I don't usually refer to "MMORPG games to correct problems in other MMORPG games", but in this situation, I have only to suggest Star Wars: The Old Republic as a good source to reflect upon when considering how a party interacts with the story, Grand Company missions, etc.

If a my party is the same job, scale the difficulty of class quests. If my party is all the same faction, let us all participate in the Grand Company leves. The ENTIRE point of Final Fantasy is parties, groups, epic battles, etc!