As for Mafia, I think they weeded out the mentally ill. The smaller gangs, or certain other ethnic one ness may have been less choosy. If even a small percent were that crazy, mafia would have had too much infighting, and way more internal wars.
Groups like Gambino and Genovese must have kept some street criminals of questionable mental stability close for when they might be needed. I don't think they let them get too close to crews, and they kept them from becoming made men.