IMHO, the men we call the Mustache Petes were basically representing the style of that day. A lot of men looked like that 100 or more years ago.
When the books were opened in the 50s, men looked differently. Not many men wore overgrown mustaches.

Is it possible that the so called mafiaban on wearing mustaches actually is a myth?
Maybe. I think it was a matter of looking proper and avoiding the resemblance of a bum. A large majority of these guys, after all, were extremely vain.