> hard part is getting countries to agree on one system
To put it bluntly, America ended WWII with a global nuclear monopoly and then only industrial base on the planet that hadn't been bombed into smithereens. That put it in a unique position to set the terms of the peace. The only party that came out with any comparable leverage was the USSR on account of its massive army and willingness to maintain a wartime economy that would have been untenable in the democracies of the West. (Absent the USSR, it's again unlikely Bretton-Woods would have emerged–the Soviet threat created an incentive to coöperate.)
More than that, the end of WWII saw American complete its then priority of decolonization. That meant there were lots of newly created countries, not quite peacefully but not at the level of violence that usually accompanies new-country formation (with obvious exceptions, e.g. Partition and Israel/Palestine), that could be wooed with riches and ideology.
Notably the USD was also rapidly losing its global share (and it had already fell under 50%) until the collapse of the USSR. Then the newly formed nations, looking to the West, rapidly dollarized, and the USD influence began growing rapidly reaching above 70% in the early 2000s when it once again began to decline to where it's at today in the mid 50% range.
To put it bluntly, America ended WWII with a global nuclear monopoly and then only industrial base on the planet that hadn't been bombed into smithereens. That put it in a unique position to set the terms of the peace. The only party that came out with any comparable leverage was the USSR on account of its massive army and willingness to maintain a wartime economy that would have been untenable in the democracies of the West. (Absent the USSR, it's again unlikely Bretton-Woods would have emerged–the Soviet threat created an incentive to coöperate.)
More than that, the end of WWII saw American complete its then priority of decolonization. That meant there were lots of newly created countries, not quite peacefully but not at the level of violence that usually accompanies new-country formation (with obvious exceptions, e.g. Partition and Israel/Palestine), that could be wooed with riches and ideology.