I don't disagree with all of your comment, but it is rather comical that you seem to be unaware of, for just one example, the US military liberating a country halfway around the world in 6 weeks, with fewer than 300 fatalities, in 1991.
That's "hard power" to a degree that no other country in human history has exhibited.
The United States retains the military capacity to conquer all but a handful of nations. Occupying, administering, and pacifying such a territory after an invasion, however, turns out to be extremely difficult, as just about everyone has discovered since the Colonial era.