So we're backing away from legal argument to conventional wisdom?
> That is the legal basis for most of the 'War on Terror' military actions
No, it's not. About the closest that comes to the truth is that a lot of the War on Terror actions are based on the legal principle that certain, mostly procedural,. Constitutional rights do not apply to actions taken by the US government overseas against non-citizens, but there is no principal under which the limitations imposed by the first amendment (“Congress shall make no law...”) don't apply to the application of a law underlying a criminal prosecution in regular US federal courts, regardless of the nationality of the defendant or the location of the crime.
> The way our system understands the law means that American citizen Anway al-Awlaki (and his son) had rights that were violated when he was killed.
That's debatable. It's fairly well established that being a US citizen does not exempt you from being targeted in war, and also that an authorization of military force requires no magic words to be a valid exercise of the power to declare war. There's a decent precedential bases that for someone not immediately engaged in active hostility, that is restrained within US territory when and where the civilian government and court system are not impaired, but there is no precedent that I am aware of creating a citizenship-based immunity to war conducted overseas.