I hope at some point in their added content they add secret places with aggroable world bosses for this little snippet I just dreamed up:

During the course of random exploring, me and my chocobo friend come across a cave hidden behind the flora of Black Shroud. Upon entering the cave I encounter some ancient long forgotten dragon, who wakes up upon smelling the scent of his favorite meal, giant yellow chickens and cat-like humanoids. I decide it best to evacuate the area quickly, and the dragon gives chase, since he's quite hungry for a thousand-year sleep.

Switch to my friends in the linkshell, waiting at a nearby Camp for me to go on a dungeon run, constantly asking in LS chat as to my whereabouts, I however am unable to answer, as I'm fleeing for my life as a giant drake rips it's way through the Gridanian undergrowth trying to turn me into miqo'te kebab.

Back to the LS party, standing around, suddenly I come dashing around a tree on my chocobo like yellow lightning, followed by the extremely large, and now extremely angry dragon, smashing down trees and stepping on marmots and getting more agitated that it's lunch can only be defined as 'fast food'. LS chat lights up with screams of WTF????'s and OMG!!!'s as they dash to their chocobos and run for their virtual pixelated lives with me at the back of the pack, hurling rocks from the back of my chocobo and hoping that somehow world bosses can be stunned by 'wrist flick'.

Eventually after circling round, and adding diremites and many other aggroable mobs to our list of 'What is currently trying to eat us' we managed to reach the transition point to Thanalan and escape.
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It'd be pointless, and offer no reward at all, but as adventures go it'd be right up there with J.R.R Tolkien XD