I agree that it would affect the US's relative dominance but I don't see why the living standards of Americans would be massively reduced. For things like medical care, housing, education etc those costs are mostly domestic so it seems like the cost of buying foreign currency wouldn't make a huge difference there. The stock market is denominated in USD so at least nominally you'd think it would be OK (although exporters would benefit over importers). Of course it would raise the price of imports, and it looks like imports average around 15% of GDP [1] and exports are around 12% of GDP [2].
So we'd need to manufacture a few % of GDP more in the US for it to balance out. That might make certain things like TVs more expensive, but technology trends have often made those sort of things dramatically less expensive, so overall (and with increased automation) hopefully that wouldn't affect the standard of living too much.
Certainly it might make it harder to attract foreign talent. But hopefully that would mostly be because of increases to the standard of living elsewhere rather than decreases to the US one.
[1] https://www.statista.com/statistics/259096/us-imports-as-a-p...
[2] https://www.statista.com/statistics/258779/us-exports-as-a-p...