If some nativist in this country had warned in 1900 that mass Italian immigration would bring us vendetta-obsessed crime clans, capable of getting their tentacles on the public life (and budgets) of major American cities while also corrupting the American labor movement for most of the coming century, he would have been dismissed, correctly, as a bigot. The oddity is that something like this happened, and, on the whole, no one seems to mind. Quite apart from the overwhelming positives of the Italian presence—the usual parade of professional eminences, from attorneys to zoologists, along with many of the best ballplayers, most of the passionate actors, all the great rhapsodic movie directors, and nearly all the (white) singers worth hearing—the existence of those bad guys, far from being seen as an excrescence, has become another positive: it has supplied our only reliable, weatherproof American mythology, one sturdy enough to sustain and resist debunking or revisionism. Cowboys turn out to be racist and settlers genocidal, and even astronauts have flaws. But mobsters come pre-disgraced, as jeans come pre-distressed; what bad thing can you say about the Mob that hasn’t been said already? So residual virtues, if any, shine bright.

You could still imagine that books debunking the Cosa Nostra, revealing a truth less glamorous if not more virtuous than what has been peddled, would be plentiful. But, where you could not get a popular historian to repeat the story of, say, Clara Barton and the American Red Cross without much close squinting and revision, a book about the Mob in New York will happily repeat the same twenty stories already known, without probing the possibility that, given the Mob’s secrecy and need for self-generated storytelling, much of what we think we know may not be remotely true. When revision does occur, it meets a stony response. David Nasaw, in “The Patriarch,” his 2012 biography of the elder Joseph Kennedy, took on one of the hardier myths of the Mob in America: that, in the nineteen-twenties, Kennedy, Sr., was a bootlegger with Mob ties, and that the ties continued into later years, playing a role in his son’s election and, perhaps, his assassination. Nasaw dismissed this as a late-arriving myth propagated by aging mobsters, one at odds with Joseph Kennedy’s single-minded goal of making his eldest son President. Kennedy, Sr., knew what would work to his advantage and what would not—and Mob involvement would not. It seems now that he was confused with another, Canadian Joseph Kennedy, who really was a bootlegger, and put his name on his bottles—with the confusion boosted by mobsters’ natural temptation to claim collaboration with the powerful. (“Senator, we’re both part of the same hypocrisy,” Michael Corleone says to the senator from Nevada; real mobsters love being able to say that, too.) Nasaw’s conclusion, in turn, annoyed the Sinatra biographer James Kaplan, in his fine life of the singer: if the Kennedys weren’t involved with the Mob, then Sinatra’s role as a middleman with the Mafia recedes in importance, and, since Sinatra’s own Mob ties turn out to be largely ornamental, with no Kennedy connection he is merely another occasional hanger-on, a stickpin rather than a stiletto. To keep Sinatra interestingly sinister, Kaplan has to debunk Nasaw’s debunking.

We all, in other words, have a lot invested in the Mafia mythology. You can still find the rare deflationary history. Robert Lacey’s “Little Man,” a 1991 biography of the legendary Meyer Lansky, known as the Mob’s moneyman, made it plain that, while quick with numbers and a good casino manager, Lansky wasn’t a genius, or much of a mobster, or even very rich. The truly smart guys didn’t run Cuban casinos; they opened Las Vegas hotels. The average unnamed businessman who bought a strip mall outside Reno must have made more money than the legendary “genius” of the Mob.

Yet it is almost impossible to demythologize the Mob. “Wiseguy,” the oral memoir of the small-time mobster Henry Hill which Nicholas Pileggi put together, and “Goodfellas,” the Scorsese movie it became, were intended to replace the myth of melancholic men of honor with the reality of street-rat scrapping. Instead, the rats themselves became legendary, and even, in a black way, lovable. Tommy DeSimone, the original of the Joe Pesci character in “Goodfellas,” was not a cute if murderous psychopath but a murderous psychopath tout court. Yet even DeSimone has become so mythologized that you can far more easily find material about his life and death than about, say, the life of Abe Beame, a small man who was the mayor of New York around the time DeSimone was doing heists. Once a myth fills some imaginative need, it becomes infinitely adaptable: King Arthur probably began as a pan-Celtic hero, then got taken up by the people he had been fighting, then got made mystical and feminized by the French Grail romances, only to end up, in Tennyson’s hands, as a melancholic Victorian. The point of a myth is to be mythical, and no amount of archeology can shake the fairy dust from its heels.