NATO countries might use mission tactics. US does not and never did.
No, from what I know that is not true. Of course, pinning down US Army tactics and operational thought from 1935 to 2023 in one phrase is... problematic.
One of the advantages the US had during WW2 was the thought the army put into how to expand itself, train soldiers and officers on an industrial scale, and generate the equipment that army could use effectively. By and large, they got it right - and wound up with an army (and marine corps) possessed of a lot of competent low-level officers and a great deal of personal initiative. Often the troops didn't follow the handbook, but they got the job done, and the better upper-level officers focused on what got done and not how.
In Vietnam you had a president who did not trust his generals (and who mostly didn't trust anyone else's competence or motivations) and a set of generals who let an amateur make decisions outside his area of competence when they should have resigned. The result was that the president got fired.
I recommend you read Colonel Harry Summers' On Strategy, a critical analysis of the Vietnam war. He makes a persuasive argument for his thesis that the US Army screwed up by having no strategy and the US government screwed up by not using the successful template of containment, Korea. Tactically, operationally and logistically, the US military was a triumph... but with bad strategy, no strategy and multiple conflicting strategies, all of that was wasted.
Famously, the US army of the first Gulf War was formed by Vietnam veterans in such a way that the mistakes of Vietnam would not recur.
Every army (and marine) publication I've seen, published since the 1930s, has emphasized initiative at the lowest levels. As with any organization, sometimes the US military gives lip service, or fails to execute its ideas, but initiative and mission-driven tactics/operations have been a part of its teaching for a long time. This is sometimes undercut by really excellent communications - it is very, very hard for superior officers to not meddle - but the doctrine calls for initiative in pursuit of mission goals, and an army is formed by its doctrine.