> The US hasn't declared a war since WWII since executive privilege allows the President to pursue war without Congress declaring war.

That's not correct. Congress no longer passes declarations of war, it passes authorizations of the use of military force (AUMF). The change was made starting in Vietnam because a declaration of war can only target a recognized sovereign nation, while an AUMF can target any state or non-state actor. The President is still heavily restricted from employing the US military without an AUMF.

I think the confusion about this stems from Congress having passed several, a couple of which are pretty broad, and never repealing them. This has allowed various Presidents to use one of the active AUMFs to justify actions, but for those who don't know or pay attention to the details it seems like the President is going around Congress.