I have read that an early draft made all handguns NFA weapons.
Yes, that is true.
Also, the Attorney General was asked if they simply banned the guns, wouldn't that be a violation of the 2nd Amendment. He answered that yes, it would be. BUT, they could tax and regulate via the tax process. Thus, the "tax stamp" was in reality a fee and license. The "tax return" was in reality a gun registration.
With the end of Prohibition, they had a bunch of Treasury agents in need of something to do, and job skills not much good for anything else... so they turned their attention to firearms.
It is interesting that corporations were specifically allowed to gain access to machine guns, yet the $200 tax, in 1934 in the midst of the Great Depression, was insurmountable for most citizens. It was a virtual ban on individual ownership of those arms.
The corporation thing was so that coal and steel companies could obtain machine guns to mow down striking workers. That was labor relations in the 30's.
Odd, in 1986, with passage of the McClure-Volkmer "Firearm Owners Protection Act" and its machine gun ban, and later, the 1994 AWB, they apparently did not get the word (from 1934) that they could not ban firearms, only tax and regulate.
Thus the theory, without a tax, they have no jurisdiction over that type of firearm.