Questing is a huge part of the leveling experience in this game, and this is a beta. I think it's the perfect time to discuss this.
It's also not about running out of exp sources, it's about the system only feeling fluid when you have quests available... which you eventually run out of. Systems like FATE and dungeons don't actually solve anything as they are available for your quested classes too. Nothing actually fills the void left by quests (and to an extent, the main story and guildhests).
I invite you to do what I did last weekend:
-Level any class to 15 via quests and doing all content available. Now try to level another class in that same region. Bonus points if it's the wrong class (ie, Lancer in Limsa).