Great question, since they obviously are contortions. Those four words are extremely clear, and yet I can't walk down to my local army surplus and buy any manner of anti-aircraft battery (which might actually be useful against those drones the army can deploy ;) ).

I think the governing circumstance is that the law is assumed to not be a suicide pact, but I lack sufficient case history to really have the zen of how common-law precedent and the US legislature has squared the circle of "shall not be infringed" vs. various licensures, taxes, and bans applied.

Perhaps worth considering is that two of the restrictions - automated rifles and sawed-off shotguns - come from an era where organized crime began out-gunning the police. This may shed light on the question.