What caused the rise of the American Empire?
IMO classical liberalism (government intentionally reducing its scope and enforcing something like common law) birthed the British and American prosperity (industrial might and technological progress) that led one and then the other to become empires. In the case of the Brits, much of their empire was formed while still basically liberal and superior organizational structures were imparted to the colonized regions, especially Singapore and Hong Kong which became fabulously wealthy.
In the case of the Americans, liberalism was gradually abandoned and the Americans instead coasted to world dominance on the back of technological and industrial power. The most successful US vassals (Germany and Japan) were the earliest in US conquest (ie while the US was still relatively liberal) and the most developed beforehand. Japan for example has very strong protections for private property in its constitution, which has led to Tokyo being among the most-affordable megacities in the world. The least successful US vassals (Ukraine, Iraq, Afghanistan, etc) are those least developed and upon whom nothing resembling classical liberalism was imposed.
If there is nothing exceptional about the middle part of North America (or the Potomac river in particular) why should the people there be the world hegemons?