I think that's a rather naive understanding of war. Look at Vietnam, look at Afghanistan. The USA still have by far the most powerful military in the world but that doesn't mean that you can just say "btw you're all your slaves now" and everybody is just going to accept it.

Maintaining a strong, authoritarian grasp on the entire world would require technology that (fortunately) did not exist during WWII and probably still not today. You'd just have civil wars, coups and terrorist attacks every other day. Your military would be spread thin across the globe. You'd basically have hundreds of countries in continuous state of insurrection like Afghanistan right now. It would cost the USA a fortune (and not just economically).

Giving these countries money in order to stabilize them and maintain "soft" influence makes a lot more sense in many cases.