For the record, questing doesn't make you learn to play your class any better than FATE grinding, because you are just learning how best to SOLO content. Solo gameplay is a completely different dynamic than group gameplay. So the only thing that would potentially "teach" people how to play the game correctly for group play would be dungeon leveling... only problem with that, you have classes like DRG and PLD that COMPLETELY change how "best" to play them between 30 to 50. a DRG goes from like a 3 button rotation, up through like 45, to an immediate change of 27 button rotation at 50. What did playing from 1 to 45 get you? how to push 3 buttons... YAY! Even the "simple" BLM is a completely different class at around 45-ish when you finally get both Bliz 3 and Fire 3 and unlock Umbral/Astral 3. So please, tell me more about how you "learn to play the class" from 1 to 45...
"Dungeons make you a better group player" - Come again? well, lets see here, a good BLM knows that they can generally AOE sleep things, fat lot of good that does you up until 36 when you finally can AOE sleep. So even your CC is a completely different dynamic for the first 2/3's of the game. But we are "learning"... Nevermind that Sleep is completely unnecessary/worthless in BC... but you know, "learning". So a dungeon would teach a BLM how to burn stuff down until 36, when he would learn to sleep things, until 50 when he would go back to just burning stuff down... Hey, if you shoot a fireball at that thing over there, it does damage! Hurray for "learning"!
Pro Tip: The actual fastest way to level is (and has been like this in just about every other game) mob grinding. Get a Full Party, with a tank, a healer or two, and the rest as much AOE as possible, chain pulling mobs in a zone at about +5 levels to your own and you will hit 50 faster than any other form of leveling (and you will actually make some money in the process because of mob item drops)