We have become so used to the addons in World of Warcraft that it would be hard to imagine playing without them. I think the leveling game would still be playable enough without addons. But could you imagine raiding without addons?
Although this appears to be a different subject, it actually links to the discussion of last week on the difficulty of WoW. Blizzard could make WoW, especially raiding, significantly more difficult in one stroke, by simply disabling addons. Several readers here commented that the kind of "hard" they want is the one requiring situational awareness and fast reaction to the events around you. That would obviously become harder if you hadn't got an addon warning you that the boss is about to launch this special attack, or even tells you to step out of the fire. And can you even imagine healing and removing debuffs in a raid without addons like healbot or decursive? My warrior significantly improved his tanking by using an addon called Tauntmaster, showing him which other group member got aggro. Take all these addons away, and grouping and raiding would become significantly harder.
Isn't it somewhat embarrassing if you are loudly shouting how easy it is to ride a bike, and then somebody points out that you still have the training wheels on?