Nothing to do with personal safety of the user/carryer: Usually un-mentioned in discussions of short-barreled is the parallel requirement that long guns have an overall length at least 26”. At the time the rule was written the M1 Carbine Paratrooper was the standard for a small rifle IE 16” barrel and 26” overall with the stock folded. The issue/concern right or wrong is concealability. Anything shorter than 26” needs to be dressed like a handgun. No folding/detachable shoulder stocks and no scattergun ( shotgun) bores. Until recent times it was always about gummint income, not safety or bans, the rules created tax income for those guns falling outside the rules-——no more—no less.
No it's about control. The laws cost more to enforce than they get in revenue.
The laws on both silencers and short rifles were "sold" on the basis that only criminals would need to conceal the sound of their shooting, with an implication of assassinations, and the same is true of short rifles, only criminal assassins would "need" them.
But of course the NFA is just as unconstitutional as any other gun control law that bans whole classes of arms from general ownership, or taxes such ownership. A tax on exercising a Constitutionally protected right, unless it's part of a broader tax, like a general sales tax, is an "infringement".