I don’t think it was a deliberate agreement per se, I feel like it was just the natural outcome after the US helped rebuild a lot of Europe. The previous world order had been ripped apart by the war, and the US was the world’s largest economy by the end.
It was deliberate, on one of the financial summits over the future of financial system after WWII a US changed all the word of GOLD to USD.
there was a planet money episode about it.
This has a link to the PMoney episode you're thinking of, as well as a more recent discussion of the economic fight other nations possibly trying to supplant or at least be adjacent to the dollar as a reserve currency.
It's the "hidden" rewards of winning the war. The US didn't take any territory (cept leaving bases behind). But they can reap the financial control and profit immensely via this indirect control.
True. The US was an industrial behemoth before even formal involvement in the War and was preposterously powerful in the area. They didn't have it diminished by bombing and gained manufacturing capacity instead of losing it.
While others were unscarred they never "stood up" by the standards of the world scale even if they were also industrialized.