I recall when visiting the WW1 battlefields finding US Army memorials to those who had fallen serving in divisions under French & UK command in the early stages, including near Ypres. IIRC there was a period when Pershing had no choice in this matter as the US build-up gained pace and for a long time, if not to the end, relied on 'X' & 'Y' from the others.

It was a working coalition, with the USA learning alongside and later separately.