When leves were reformed so that they would no longer be central leveling content,
Yoshi-P announced this change in design philosophy:
"We still have some ways to go, but FINAL FANTASY XIV will gradually shift from being a grind-centric game to one that offers enjoyment for all playing styles and circumstances with its ever-expanding variety of content."
It sounded like FFXIV was going to move toward a leveling model that would bring it in line with modern MMOs. Players would be able to take on "large volumes of quests" that required actual interaction with NPCs. These quests were indeed described as a viable leveling tool when it was said that, "In addition to guildleves, sidequests will also be made to yield skill points upon completion, thus providing players with more avenues for advancement."
This obviously has not fully come to fruition, as quest rewards are minimal and the number of quests are insufficient to really progress your character. While the new leveling model implied perhaps some WoW-style or Aion-style questing (which I would personally love to see), that doesn't seem to be something that's coming anytime soon. Perhaps this is in the works for 2.0. I wouldn't be surprised if they held off until then, considering the large-scale changes to maps and zone progression that will be coming. A lot of the quest writing and hub setup would all change, with a lot work wasted.