When it comes to violent crime, Italy doesn’t exactly have the best reputation. A glance at the stats reveals a different story.
You're correct about the close link between vodka binge drinking and homicides in Eastern Europe. Classical Russian homicide in the 1990-2000s era: Man in 40s knifed in apartment during multi-day zapoi. Typical American homicide: Man in 20s killed shot in gangland dispute.
Re-Italy, I'd also add that the Mafia probably keeps crime monopolized to itself to some extent, which also makes it less likely for authorities to heavily crack down on it. Also in the least functional parts of Europe murders might not get reported as such as stringently as they would in Northern Europe, through this is purely hypothetical (demographer Alexey Raksha argues this applies to a significant degree in Russia).
The U.S. Mafia was less violent than more recent criminal organizations. If you owed them money, they would threaten you or rough you up; but not kill you because that wasn't going to resolve the debt. Likewise they would bribe or blackmail law enforcement and politicians but not commit killings, assaults or kidnappings because of the likely response. The more extreme forms of violence were between families, or to maintain internal discipline and loyalty.
Allow me to interject with one curious fact to add to your point about the reputation – or rather, the narration – being really detached from actual data and one small correction about your second factor.
With the lowest female homicide rate in Western Europe, we are possibly one of the safest countries for a woman to live in. But the situation is made to look terrible by the very Italian press, keen to use the word "femminicidio" – femicide: a woman being killed for "sexist reasons", whatever that means – to describe basically any homicide involving a woman. Ask around, and many good-thinkers here will tell you we have a national emergency, despite there being none. The very Italian National Institute of Statistics will make alarming remarks, while also providing data that shows the opposite picture despite the extremely shady way it's collected.
Now, about the correction: I really wish we had the low immigration rate from Africa you talk about. Unfortunately, those numbers only account for LEGAL immigration. We are actually one of the European countries with the highest estimated number of irregular immigrants: between 500.000 and 700.000, basically one every hundred citizens. The situations is dire, indeed.
So what may be an alternative second factor? Take my random word for what it's worth, but a common adage we have here that is that where the Mafia has the most grip, other people commit fewer crimes in order not to get noticed. Migrants really seem to be more fearless and cause more trouble in the city of Milan in Northern Italy, where they have to respond to the police, than in the city of Reggio Calabria in Southern Italy, where they have to respond to the local organized crime overlords.
People are saying that the Mafia enforce law and order but that doesn't explain why Italy murder rate was higher in the 90's than now. It also doesn't explain why Latin American countries with heavy cartel presences have high murder rates. I think it is more likely the three reasons the author gave.
I think the answer is that no one knows for sure, because the evidence isn't there. The Mafia has always wanted to portray itself as a protector of local communities, but that's never been true - it's ruthlessly self-interested to its core.
Interestingly (or at least I found it so) it's origins are likely to be in modernity, and industrialised agriculture - after the British Royal Navy decided on citrus fruit as its preventative of choice for scurvy it started sourcing vast amounts of them from Sicily, and the combination of the money to be made and the reliance of the harvest on irrigation (which was easily sabotaged) made the industry vulnerable to extortion by organised criminals.
Which would seem to argue against the Mafia originating as some form of local self-defense organisation - though you would have thought that Sicily's history of centuries of appalling, rapacious misgovernment by foreigners still has some role to play.
Also true on regional level - provinces with younger population and more immigrants have higher crime rates:
Given this information, what role does the Mafia play in influencing law an order in society? When the mafia started out (just as the China Town Tongs in the United States started out) there was elements of ordering society and protecting people before the organization eventually fell into a crime/gang syndicate.
I've always wondered if Religion had any part in it not being so violent.
The picture we Americans have of the Mafiaso is that of gangsters who commit crimes on the weekdays and attend mass on Saturday and Sunday.
Isn't it obvious: they have a low murder rate because the Mob has a monopoly on liquidations; it won't permit competition
Murders provoke a political response, like in 1992 assassinations of Falcone e Borsellino. The mob usually avoid assassinations...of they make the body dissolve.