I don't want to get too deep in the weeds with Amity Schlaes on the gold standard but her praise of the Bretton-Woods system is more interesting because the strong performance of the world economy during that era attracts a lot of praise from different ideological sides. I wouldn't even characterize it as a gold standard system at all nearly so much as a "dollar standard" with pegged exchange rate. But however you characterize is it, the thing that Bretton-Woods nostalgics tend to forget is that the Nixon administration didn't abandon it as part of some pet ideological scheme.
It fell apart because the system was unworkable and unsustainable—its operations required a level of U.S. economy hegemony within the capitalist bloc that was appropriate to the 1950s but didn't reflect reality once postwar rebuilding occurred in Europe and Japan. Things were looking very raggedy by the end of the Johnson administration, and when Nixon finally pulled the plug it was because he had no choice. It is true that the Bretton-Woods years were prosperous, and it's even arguably true that the Bretton-Woods system contributed to that prosperity for much of its life. But it was dropped because it stopped working. The United States couldn't retain the volume of gold reserves needed to make the system work without the active cooperation of our major trade partners and they didn't want to cooperate. And that's just a specific case of the general point that you can't have a multilateral system of fixed exchange rates unless all the participants agree on what to do. The circumstances of the early Cold War facilitated that level of agreement, but it's a really hard trick to pull off.