https://ammo.com/research/list-of-banned-guns-and-ammo-by-st...
Sawed off shotguns seems arbitrary and that was ultimately my (pre-coffee) point; government is fine with coming up with an arbitrary restriction when they want.
They could outlaw the means of production. Gen pop is not allowed to own that.
There is, in fact, a good question wrt how much of NFA is actually constitutional. A funny thing about this is that ATF has dropped cases on several occasions where the defendant tried this angle, presumably because they didn't want something contrary to their current regulations as written to be overturned in court, and because they had plenty of other charges to throw at those guys anyway.