I always thought of the Avengers as the squeaky-cleaner good guys
Just playing devil's advocate. I'm not excited for Wolverine (nor Bendis for that matter) to be on Avengers, unless they pull him out of the entire X-universe, but they won't, because being on 4 teams at the same time makes sense. Anyways.
The Avenger have included in their roster several not so squeaky clean people.
Former terrorists (Quicksilver and Scarlet Witch).
The living embodiment of property damage (Hulk),
Former criminals/mercenaries (Hawkeye, Swordsman, Sand Man, Moon Knight, Black Widow, Wonder Man, Ant Man II)
Murderers (Jim Hammond, USAgent, Captain America, and I'm assuming as a legendary space soldier Mar-Vell took a life or two at one point, as well as Thor, Hercules and Gilgamesh most likely, and perhaps Dane Whitman as he did go back in time and serve through the crusades in medieval Europe)
Pimps and drug dealers (Falcon, as horrible as his pimp retcon was)
Prostitutes (Mantis)
Really mean snooty bitches (Moondragon)
And other members who have morally ambiguous pasts, i.e. Triathalon getting kicked out of the olympics because of steroids, Stark being a weapons designer. Heck, any given line up could have members with more legal trouble than some of the Thunderbolts.
And one of their associates also happens to be the SON OF SATAN, who's not a very nice guy anymore, although to be fair at the time of their association he was a real nice chap.
But again, I do see where Wolverine being an Avengers isn't exactly a fun time. I think the Avengers should have a few new by-laws, such as no redundant members (2 enhanced street level fighters--Cap and Wolverine, now in a sticky situation where Cap would have been taken out before, but other Avengers surviving because of various reasons, you'll have 2 characters taken out by the same threat) That's just my idea though.