Why do you think the American public is so entranced by films about the mafia and other forms of organized crime?
Americans have always been drawn to depictions of criminals. They like people who (they feel) are living life in their own way, according to their own code of honor. I believe that this is why they like films about the mafia.
We Americans feel that we are a nation of non-conformists. We feel that we are people who are willing to stand up for what we believe in, regardless of what the law says. The mafia seems to us like it represents this sort of independent spirit that does not simply give in to doing what the society says we should.
Finally, I think that we (men especially) want to feel that we are tough. We are people who take our problems into our own hands and do not need others to solve them for us. I think this is one reason why we are attracted to the mafia. They take care of their own problems in a way that shows that they are very "manly" and self-sufficient.
I'd suggest that the popularity of this genre might have more to do with predictable story types than it does with the content of the stories. People enjoy predictable media. That's why formula cop shows and hospital dramas are so popular, in my opinion.
So, my response would be that Mafia Movies are a defined genre, like Westerns, and that is why they are so popular. However, I realize that leaves open the question of why Mafia Movies are more popular than Westerns.
To that question I'd simply say one type of film is contemporary and relatable and the other is a bit out-dated.