The Unknown!

[Hulan]

There is certainly precedent for this in FFXIV. More to the point, you say "quests" but this same itch can also be scratched with any number of "secret" content. For example, "secret" revealing conversations that give you insight into a location, person, or nation. For instance, did you know that the Amalj'aa dig up the bodies of dead, embalmed Ul'dahians, and cover their weapons in the embalming fluids to prevent them from rusting?

Things like the aforementioned Wandering Minstrel, Imperial Attacks, etc go to show that they do have some of this in mind already. Though mystery can be a double edged sword, posting obligatory FFXI reference: