I actually like the idea of levequests. In theory. There's a lot of things I like about Final Fantasy XIV, in theory. Sadly, then we get to the actual implementation of things, and everything just kind of all falls apart.
First, I have to explain what I'm assuming the mechanics of a levequest are supposed to be. Sadly, there are a lot of mechanics in Final Fantasy XIV that need to be examined to see what they're supposed to accomplish versus what they actually accomplish. And, of course, I'm guessing at what they're supposed to accomplish. I can't actually know. Also, my assumptions are based on the idea that the development team aren't made up of complete morons, an assumption that the game's launch leaves somewhat dubious at best.
In any case, I'm assuming that levequests are intended to be a time-limited method of allowing "casual" players to keep up with "hard core" players. The idea is simple: they provide a nice advancement and money/item boost that's time limited. Casual players can use them to quickly advance without worrying about the time limit. Hard core players burn through them quickly and then move on to other content.
Players of the game will instantly notice the problem with that last sentence. I said "move on to other content."
There isn't any.
Sure, you have the main quest line, but that's very brief. You run through it, advance the story, and are then told to go level up some more before you can continue. Then there are the side quests that were recently added. These are WoW-style quests: a brief bit of text, which leads to killing mobs/running to points on the map to gather MacGuffins for the quest giver. You gain no XP from these, so the only point to do these is for the items given. You're certainly not doing them for the story, since the "story" is a large block of text with little to no relation to the actual game world.
That leaves the one other way to advance in the game: behests. Behests are a giant clump of PCs forming a team for about 20 minutes max, running around, blitzing mobs, and then immediately leaving. They're chaotic, they require no skill behind hitting the "attack" button repeatedly, and they're honestly quite boring.
Which means, ultimately, that instead of the levequests being content that allows casuals to keep pace with hard core players, they're essentially the only thing to do in the game. And they're time limited, so once you've completed them, the only thing to do is to log out and wait for them to reset.
Something that most casual players will probably run into, since there are quite a few "weekend warriors" who can only spend a few hours playing on the weekend - and they'll hit that time limit just as easily as the hard core players who can spend those few hours every night.
Weirdly Enough...
...Now that we're in A Realm Reborn and there's a ton of other crap to do, levequests actually work quite well. Ish. For crafting and gathering classes.
Unfortunately they're kind of useless for combat classes, primarily because the rewards for other content are just flat-out better. But still - they actually do work in a game that's not completely terrible!