I would think it started because they wanted everyone to pass for legitimate business men. So that would have meant having a clean-cut appearance. And I don't mean to denigrate anyone in law enforcement, but I think police do tend to observe people's appearance and whether it fits the pattern of people they've arrested previously. So a guy who looks like a clean cut small business guy or working stiff will get less scrutiny than a guy who looks like a "hippie" or a biker. And the Mob is an authoritarian, almost military like gang, organizations like that tend to make up strict rules about how the members are supposed to look and act.