The real reason was that FDR and his minions were scared of a revolution. The gangster era was the excuse, not the reason. They knew what happens to leaders after a revolution, and the idea of revolution was in the air after the depression and access to power by Hitler, Mussolini and other revolutionaries. For all FDR's claim of supporting the common man, he was a child of wealth, and he had no intention of keeping company thugs and state enforcers from getting all the guns they wanted; but he wanted to disarm that "common man" he claimed to love so much, and who really terrified him.
There is already a drumbeat of rising hysteria about Jihadists in our midst, and a lot of it is coming from the same old gun control gang that worked up scares over guns in the hands of blacks, Mafia hit men, female assassins, radical "Commies", right-wing extremists, etc. No matter what the threat, real or invented, the answer from the anti-gun gangsters is always the same - ban guns. They are even using "climate change" to promote gun control, claiming that "coming outbreaks of violence over dwindling food supplies" justify the "need" to ban guns, except, of course, for the police and military.
Jim