The National firearms act of 1934 originally lumped in handguns with full auto firearms. It is clear that the Roosevelt administration wanted to subject pistols and revolvers to the same draconian regulations and taxes that machine guns were finally subjected to. Congress simply would not go along. It was a step too far for even the heavily Democrat Congress of 1934.
Once you understand that
licensing of handguns to the point of prohibition was the major target
of the legislation, the reason for including short barreled rifles and shotguns becomes clear. What is the point of banning handguns if any
person can buy a rifle or shotgun, a hacksaw, and make a functional
pistol in fifteen minutes from that rifle or shotgun?