I guess this explanation is flattering to US citizens but actually the reverse is happening: https://en.wikipedia.org/wiki/Triffin_dilemma. Due to reserve currency status of the US dollar, there is additional external demand for dollars. This means that the US will necessarily experience a trade deficit, importing more goods from other countries than exporting US goods to them.

> Why are these American dollars valuable to you?

You need them to service your dollar-denominated debt or to put them in your reserves.