The reason was Sawed off shotguns were already recognized as a tool of the criminal as were cut down rifles. There simply were no such things as ineligible people until the creation of the "prohibited persons" catagory under the 1968 GCA.
No, I wish people wouldn't just adopt logic that sounds good today.
Politicians and various people such as the Brady bunch always go on record saying stupid things, sometimes generations later people take it as having been fact.
The real reason cut down long arms were outlawed was because handguns were listed to be outlawed in the NFA. In fact handguns were the primary purpose of the NFA, machineguns were just a secondary bonus included due to concerns over ww1 vets.
The reason handguns were the target was handguns were used in the majority of crimes just like today, they also however have a lot of support from the population because they are the most used firearm in defense as well.
So the primary purpose of the NFA was to outlaw handguns. The tax was designed to put the listed firearms out of reach of most, as it was the great depression and $200 was a lot of money then, involving a process most could not simply research on the internet or the local library.
At the time the federal government did not believe it had the constitutional authority to outlaw anything, merely to tax, so they chose to outlaw through taxation. They did the same thing to outlaw drugs for example which they also did not believe they had the legal authority to outlaw.
Even the NFA was felt unconstitional by most judges as it targeted a specific right and that was the national consenses as is seen in the Miller case a few years later and in commentary by judges throughout the nation on the case. Even most of those that agreed with the aim of the NFA felt it was unconstitional. Even the Supreme Court did not uphold the NFA then, Miller simply died and nobody showed up to prove his case before the Supreme Court. The Justices could not legaly consider evidence never formaly entered and had to rely on the prosecution's side exclusively.
In fact the justices in thier wording even acknowledge Miller would have prevailed if someone could present evidence the items in question had military purpose IE suitable for the militia. Short barreled shotguns most certainly were used in ww1 so it goes without saying that had Miller survived or even someone argued on his behalf the NFA would have been thrown out. Nobody did though.
Since the primary purpose of the NFA was to outlaw handguns they couldn't have people simply cutting down longarms to replace them. So additional measures such as restrictions on reducing the size of longarms was added to compliment the handgun "ban".
When at the last moment handguns were removed from the legislation the complimentary portions restricting long arm dimensions were left in as an oversight.
Since that time various people have invented logic that sounds good today but was not the purpose or intent at the time. The purpose was so people would not still essentialy be able to make handguns from longarms when handguns were banned.
Further much of the restrictions that exist in the NFA today were added much later by legislation such as the 1968 GCA. Destructive devices for example limiting caliber to .50 and below were added at that point. So even though they are part of a 1934 law they were added many years afterwards further clouding understanding of the history of the legislation.
The NFA was a handgun ban. They attached machineguns to the handgun ban, but handguns were the primary target. Most machineguns famously used by criminals were actualy stolen from police or military and the legislation would not have even had much effect.
Handguns were removed from the handgun ban, but the antis ever mindful to get what they can still pushed the leftovers through.
The public was sold the BS legislation as an anti-crime bill but the real reasons for the machinegun addition to the handgun ban were concerns of those in power at the time.
The truth is WW1 vets promised many things were being screwed over by the government. When the vets peacefully marched on washington and camped outside the capitol those in power wanted to add machineguns to the handgun ban. Especialy since they used tanks to break them up. Even after they cheered the arrival of the military, thinking it was a parade celebrating thier cause. Imagine thier surprise.
The government did not want upset vets with lots of military experience legaly able to have machineguns afterwards. Keep in mind this is a time when trench warfare is still the name of the military game, so machineguns are an extremely formidable weapon in the hands of trained veterans.
