[Leves are] XIV's version of FFXI's Fields/Grounds of Valor, more or less. From what I hear, that was well-received in XI.
Leves are indeed FFXIV's of Fields of Valour, and it happens that FFXIV's version is terrible, mostly due to the overbearing presence it has in the game. I'll elaborate:
Unlike leves, Fields of Valour wasn't a central part of FFXI's design. FoV took the form of innocuous little books tucked somewhere in a zone rather than huge campsites comprising a majority of a maps' landmarks. Furthermore, FoV was a once-a-day bonus, a useful supplemental reward on top of what you were already doing, whereas in FFXIV it was just about the only thing you were doing -- the main focus, as it were.
FoV, perhaps because of its innocuousness, was actually so much more lore-friendly: rather than re-capture that same escaped Imp 36 times (as another poster mentioned), you just train yourself by focusing on certain species of monsters; rather than re-clear the land of the same crop-eating respawning dodos 36 times, you just train yourself by focusing on certain species of monsters. FoV was simple, but certainly effective; its reason for being justified itself quite well.
The fact that FoV was merely laid on top of FFXI's already rich environment made it much more interesting to complete, at that. Rather than FFXIV's penchant for having the UI mark with a huge red circle the monsters I need to beat, which would invariably appear quite close to me as soon as I accept the objective, in FFXI I would have to select a FoV page and then actually look for them! Maybe I have to kill a bat for a FoV objective -- well, I'd better check caves, or perhaps wait until night, and maybe I'd start to make a nice routine for myself, get to know the lay of the land, or discover a neat nook for myself that allowed me to train with a great efficiency. Not so in FFXIV, whose leves truly are little more than a game of follow-the-arrow with a wall-of-text thrown on top that, after the first time completing it, usually doesn't even make sense anymore.
In short: make leves simple, keep them in the background, and they'll be a nice supplement to a vibrant world. Make leves central, have the game revolve around their repeated completion, and their weak foundations and countless flaws will show through very quickly.