Despite being an Olympian, Hercules has always seemed a bit out of place and not just due to being originally a demigod. Yes, he comes there for a place to sleep and party, but he is so different from the other Olympians it seems he would fit in better with Asgard or The Celtic Gods of Avalon. There overall culktures are more of the warrior/advenurous type that Hercules fits instead of hte hedonists of the Olympians. Would Hercules be better off trying to become a member of the Asgardian pantheon?
For that matter, among the reasons Hercules often wanders from Olympus: thirst for adventure, lust for life, spread his fame, etc,. do you think another reason is just to get away from his family. Because if you think about how pretty much all of the major ones are either massive jerks or have one too many moments of behavior like that and how they may look down on Herc for being formerly mortal I can't help but think that though he has learned to tolerate them part of him gets tired of all their crap?