Evan as a Non-Consumer of alcoholic beverages I will still have to say, the Repeal of Prohibition in 1933 had a far greater impact on curbing the use of those "Classes of Firearms" than did the 1934 Federal Firearms Act.
After 1933 about the only market for Illegal Liquor was from the Hill-Billy MoonShiners & they weren't using "Thompsons & BARs".
There are still some of these around but for the most part they are not the violent type. They just like to make a bit of Shine for tham as likes it.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra