When it first appeared, quest heavy advancement was hailed as a relief from the "mob grind" prevalent in DIKU style MMORPGs. But different does not always mean better. The quest grind has turned out to be little different than a mob grind, and in some ways it is worse. And oh my, the walking...
A lot of MMO gamers are probably reading this and are already reaching for the pitchforks and torches. I implore you to read the entire article and look at the subject from a new perspective. This article was inspired by a post on my blog, Muckbeast. Reader response was so overwhelming, I knew the subject deserved a more detailed examination.
Questing was praised as the solution to the tedium of mob grinding. World of Warcraft, of course, is at the forefront of this movement. Every zone or town has one or more "hubs" with merchants and quest givers. The quests then cause you to move about the zone doing this or that task, killing X of Y mob, gathering A of B items, and the like. The idea was to give players a story and a reason behind all of their actions, rather than just running from place to place killing every mobbie they saw. In some ways this system has been a success, but in many others it has been an abject failure.
This question summarizes what quest heavy advancement has become. While researching for this article, something very similar to that phrase was the most ideal search phrase. Sad, isn't it? The point of quest based advancement was supposed to be a focus on story and a movement of the player away from single minded focus on reaching the level cap. So much for that idea.

Sorry to give away the ending, but this part of the article is far shorter than the parts that talk about where quest heavy gaming went wrong.
Many quests in games like WoW are actually very good. They have interesting story lines. They have characters you care about. You can find yourself moving forward to advance the story or to help out an NPC you feel an affinity towards. Those are all good things.
WoW-style quest design keeps players moving from zone to zone and avoids the "where do I go next?" problem. As you finish all the quests in a hub, the quest givers start asking you to visit NPCs in the next zone over. This pushes you along at approximately the right level to move along. This is a helpful and effective way to keep players progressing through a world's content.
Finally, quest heavy advancement does effectively create the illusion that you are not simply grinding mobs - for a time, at least. Eventually, it becomes obvious you are still grinding, you just do a lot of running back and forth after every 10 to 20 mobs you kill. Oh wait, this is supposed to be the good stuff.