Vamp - nobody sits around and waits for a group unless they're trying to do something out of a select list of quests and activities that nobody can *really* do alone. Nobody can solo most elite quests at a semi-reasonable level. Nobody can fight into and through Scarlet Monastery and kill the bosses there without using exploits. (This was the place to be for farmers.)
Otoh, people aren't afraid to make groups to make doing certain non-elite quests easier on them. I have to kill 8 Shambling Skeletons, and so does this guy I'm fighting over the spawns for? Simple solution. You both get credit for each kill while grouped, and each goes by smoother with a second person helping.
Grouping is not required for at least 70% of the material in the game. Soloing is not more desirable for most of that 70%.
As for doing things with a group other than questing, yes sometimes. People who want to explore a new zone, particularly an intriguing but nasty cave, or who want to farm an instanced dungeon (like Scarlet Monastery,) will just run around killing stuff. Truth be told, this is usually more for the benefit of seeing items drop than it is for gaining exp.
Blizzard has been very careful to tune out the mindset that the best way to level is to endlessly kill the same creatures over and over again. Because of the quest rewards - exp and loot - and the implementation of the rest states, (which is still being fine tuned and still broken,) the game does not lend itself to mindless slaughter. Which is good...I think my retinas are burned from how many hours I sat in Velk's Lab fighting white spiders on a white ledge in a white cave for 90+ hours across one week. (But darnit, I got from level 53 to 59 in that week!)
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Only the exceptions can be exceptional.