(OTOH, this is a discussion specifically about American action, anyway.)
If you are of the opinion that this is not the case then maybe America should withdraw from the Geneva convention and various other useful treaties as well because after all, what's the point in having rules of engagement if you're going to ignore them anyway...
Yeah, but declarations of war (whether with or without magic words) aren't really important in a legal sense in that domain. Alexander Hamilton observed that they were falling out of use internstionally before the US Constitution was ratified, and the post-WWII international order has essentially made them moot with the recognition of aggressive war as a crime against peace. Fighting a defensive war once hostility was initiated (or, perhaps, clearly imminent) has long been accepted as valid with or without declaration, so with aggressive war itself a crime, there is no war legitimized by a formal declaration.
The international laws governing armed conflict are operative based on the fact of such conflict and the identity of the parties to it, not declarations of war.
That's the whole reason the Geneva convention was created to begin with, to differentiate between combatants and non-combatants. Now, it absolutely sucks that the other party doesn't play by the rules but that is no reason to stop playing by those rules ourselves. The moment we do so we stoop to that same level.
Anyway, that's a past station by this point and I'll probably have a hard time convincing you that on the evening of 9/11/2001 America had the keys to a new world order in its hands and squandered the opportunity by seeking petty revenge and economic advantage. The lesson learned that evening is that by doing what your enemy wants you to do you lose, big time. You can't wage war on ideas or on reactions.
Both the US and each of the groups it had targeted under the 9/11 AUMF has an identity.
Some of the targets are parts of diffuse groups with little central command structure, which makes it very hard to end a war against them (and harder still to draw and end to an open ended war where targets are added by loose association), which is a problem of the crafting of the AUMF, it's continuation in effect, and the Congressional oversight of the war effort.
In an international law sense, there's a host of valid questions about the adequacy and appropriateness of the rules governing conflicts involving non-state actors (such as Common Article 3 of the Geneva Conventions.)
> Now, it absolutely sucks that the other party doesn't play by the rules but that is no reason to stop playing by those rules ourselves.
I don't disagree, but drone strikes per se aren't a violation of the rules.
> I'll probably have a hard time convincing you that on the evening of 9/11/2001 America had the keys to a new world order in its hands
Well, yeah, that's a claim that would take some support.
> and squandered the opportunity by seeking petty revenge and economic advantage.
While I doubt the existence of the opportunity you suggest was squandered, I do think the US government did a grave disservice to both itself and the world community with it's conduct in the years immediately following 9/11, most especially, but not exclusively, in the naked war of aggression it leveraged domestic outrage at 9/11 to justify in Iraq.
And I think there are deep problems with the broader “War on Terror”, I just seem to disagree with you on the degree to which those problems are due to violations of clear proscriptions in international law or failure to observe ceremonial requirements.
If you want an example of an actual exercise of Congressional power to declare war that applies (conditioned on Presidential determination) to both state and non-state actors, see the 9/11 AUMF.
IOW, been there, done that, and that's what got us where we are.