Even LFR or random heroic dungeons or scenarios are group dependent, it's just that in these cases the groups are assembled for you by the game. You may well queue up for each of these alone, and you may leave and go about your business afterwards just as alone, but the actual raid, dungeon or scenario will have other players in it with you. This is an inescapable, inseparable part of the WoW experience, and it is one of the things I enjoy about the game.
However, as much as I do enjoy group activities, as much as I love raiding and going into a dungeon or raid zone with a group, there are times I just want to be alone. And it is this desire to sometimes play at my own pace, to my own schedule, that has me reconsidering my expansion-long disdain for the daily quest structure of World of Warcraft.