Umh. That's exactly what I'm saying Randis.
That kind of content already exists in several games (and partly in FFXIV as well). But as you said the cutscene/storytelling part is seen as each player is the protagonist, with the NPCs talking directly to the player put in a leading role on his own screen, and talking with the others in the same role on their screens.
While fights and traveling happen in a shared world, cutscenes happen in an incompatible vacuum, which is entirely acceptable, and in no ways incompatible with each player's character being portrayed as a main character on his own screen.