They didn't want to assimilate, lose their culture, be America's bitch or be the bitch of guys worse than them.
Are you referring to the Mustache Petes, or the Young Turks who formed the mob as we know it?
The founder of the modern day mob, Lucky Luciano, couldn't care less about his culture. His culture was money. The old school Sicilians didn't like it, and he rolled them.