The answer is very simple: domestic politics.
President Wilson feared two things:
1) That the Allies would use the untrained and badly equipped troops as cannon fodder.
2) That US troops under foreign command would lead to public outcry.
So far, US troops had only been placed under foreign command once (US Navy at Shanghai Station under British command in 1900). This was not well received in the American press back then.
Now in reality, General Pershing, in his wisdom, realized that Allied help was needed to properly train and equip the American Expeditionary Force.
The French trained and equipped the American troops and even integrated coloured American troops in French front line units as the US Army was strictly segregated.
The US troops fought in reality under French command (and some under Belgian command as well) although the French orders were officially issued as 'suggestions' to limit political fallout in the US.
The trick worked.