They were doing the front boss thing while other families were suffering from internecine warfare over who would be the boss. This way their real hierarchy remained insulated.
Insulation of the boss seems to be the common thread between the successful families. Here's what the Chicago Outfit was involved in while Tony Accardo was "retired"/cosigliere:
- Rigging a presidential election
- A plot to kill Fidel Castro (Operation Mongoose)
- Multi-million dollar casino skim in Vegas
- A ton of circumstantial evidence suggesting the involvement of the assassination of a U.S. president
Giancanna, Joey Doves, and others take the heat while Accardo eventually dies an old man at home, having spent 1 night in jail in his entire life.