US is prosperous because it produces the world currency. Need to buy steel? Just print more dollars and buy it from any other country. Need to buy food? Ditto. Need to buy brains? Ditto.
No working is required, when you can print any amount of currency and can buy anything from any part of the world with it. Yes, printing speed up inflation a bit, but unlike in any other country of the world, when US is printing dollars, they spread the effects of inflation on all of the world: US becomes richer and all other countries a bit poorer.
This is why linking dollar to the gold would kill US prosperity. Also, one reason is why US is so heavily militarized and is fighting wars all over the world: you need to constantly threaten all the world so that they can't even think of choosing any other mean for world trade other than dollar.