The times dictated the legislation. Organized crime had taken over vities in the 2ps. These criminals availed themselves of all sirts of exotic weaponry. Silencers were considered, like Tommy Guns and sawed offs to be the tools of the trade for these criminals. Cops were often outgunned if they were a mind to confront the lawlessness. So silencers, the tools of furtive killings, and sawed offs, and Tommy Guns, and other AWs like BARs were declared illegal. O Tempora O Mores.
That is the narrative that we have been sold, but it is not true. There were no assassinations with silencers even mentioned when the ban was passed. Nearly all the full auto weapons used by gangsters (which was a very, very rare occurrence) were stolen from national guard armories. Sawed off rifles and shotguns were outlawed because the authorities wanted to outlaw pistols. It made no sense to outlaw pistols if anyone could make a pistol from a rifle or shotgun with a hacksaw and 15 minutes time. So sawed off shotguns and pistols were included in the law. When pistols were taken out, the sawed offs were left in, almost by accident, because few people cared about them.