The Gangsters were the reason given for passage of the NFA.
However many of the most notorious gangsters actually obtained thier full auto weapons from police and military armories, they didn't purchase them. So it would have had minimal impact on them in reality. We have created a list of them before. Many were stolen from national guard armories and police. Tommy guns were actually a police gun more than a gangster gun, though today they are with being a gangster gun, back then they were more popular and common with police than gangsters. So most that gangsters had were obtained from police through daring raids, theft, or corruption. While 1918 BARs were widespread in National Guard armories, also targeted by gangsters. Just as today the official reason given in the media or by politicians for public support can be misleading. The public is manipulated.
Gangsters played some role, but thier role was greatly exaggerated to manipulate and pass legislation.
The more realistic reason was the Bonus Army.
The Bonus Army scared Washington, and Congress was sneaking around in subterranean tunnels to avoid them.
FDR (who would be in power when the NFA was passed) was in DC at the time as well though he was not President yet.
It was thousands of WW1 Veterans, at a time when trench warfare was still considered a primary method of fighting. They were desperate experienced veterans who were routed with rather excessive force.
Thier movement was felt to be a bit left leaning.
This was also only a little over a decade after the Communists had had the October Revolution in Russia, a first demonstration of the lower class rising up and taking over, and that was something that still scared many governments and Capitalists, and especially those with the most to lose (who tend to have the biggest influence in our government.)
While the US was suffering through the Great Depression, and Communism would have had potentially its highest appeal level to average citizens.
It all combined to create a mindset that needed to insure these types of people, experienced people that knew how to fight, at a time when machineguns in trench warfare were exceedingly powerful, could not just go purchase machineguns or a variety of weapons.
Douglas MacArthur attacked them and drove them from the Capitol with tanks. At first the veterans cheered at his arrival, thinking it was a military parade in thier honor. Imagine thier surprise.
No, those tanks were there to be used against them.
But such a group in the future could return, and if they came back well armed, at a time when trench warfare dominated, it could be very bad.
However demonizing a bunch of desperate veterans when much of the nation could relate to them was not politically viable at the time. Driving them out with brute force meant they would have even more sympathy.
Gangsters on the other hand, most could agree gangsters were bad.
So gangsters were the official reason for the NFA.
However even when the NFA was passed most believed it was a temporary measure because it would be struck down as unconstitutional when it got around to review. That was a general sentiment at the time of many judges and politicians, even those that liked the NFA did not think it would pass Constitutional review.
They were correct, Miller went pretty far in that direction, all but saying that had it been a machinegun instead of a short barreled shotgun they would have ruled it a weapon suitable for militia use and protected by the 2nd Amendment, but without evidence offered that a short barreled shotgun was useful in a militant capacity (the plantiff died so nobody submitted evidence on his behalf or argued on his behalf) they couldn't rule it was protected. (Had he had representation they would have shown shotguns used in WW1.)
The Miller case showed the sentiment at the time.
Nobody believed the NFA would stand around that decade, but it gained defacto legitimacy by going decades with no review and becoming a common staple in law. Over time it gained legitimacy simply by being.
By the time of Heller it had been in place so long without review that they didn't want to shake things up too much.
Another key destruction of the 2nd Amendment was the addition of prohibited persons in the 1968 GCA. While on the surface it certainly is nice to not want dangerous people to have guns, and is something with widespread acceptance, in reality it means nobody really has the protection the 2nd Amendment was meant to provide. For if anyone really clashes with government they will find themselves a felon, whether from clashing with police, or civil disobedience, or something less obvious like tax or white collar charges when the government goes over them with a fine toothed comb to find anything they can charge a thorn in thier side with. And they will not legally be allowed to have firearms.
So the very types of things likely to happen as tyranny took hold, before things got that bad, would cause many of those active in opposing tyranny through political means and demonstrations to be prohibited persons. In fact you only need to look towards the Civil Rights era (the same era the GCA was passed in) to see the truth of that, as various demonstrators and activists were charged for a variety of things that with the prohibited person statute in place would prevent them from being legal gun owners.