Funny this just came up because i was wondering the reasons behind it myself. One thought is that if the LCN is based on the old Roman empire days, then it would follow that facial hair wasn't allowed because the Romans rarely grew out beards unless in time of mourning (I believe). So I think it was just an offshoot from that. I think it was Emperor Hadrian was the first of the Caesars to actually have a beard.
I don't think the mobsters were that sophisticated. It was just an attempt to look like legit businessmen.
