There’s no real logic involved.
From what I can remember, the sawed-off shotgun was a weapon favored by bootleggers back in the 20’s because it seemed scary & didn’t require precise aim, so they banned it and somebody decided the same type of rule should apply to rifles as well — like the Thompson, which was also popular with gangsters of the day. The 16” barrel length is just an arbitrary thing some doofus came up with.
Correction
One major change to the NFA came in 1968, when the minimum legal barrel length for rifles was dropped form 18 inches to 16 inches. Why? Because the government had already sold a quarter million M1 Carbines – with illegally-short barrels – to private citizens, thus rendering them all felons. Instead of trying to enforce a clearly irrational law, Congress reduced the barrel length stipulation.