In connection with my project on why America lacks a ceremonial head of state, consider one flawed perspective. The Framers could not have understood the value of such an executive division because there were no models or precedents. Yes the Crown and the Cabinet were separate, but that arrangement was in its early stages and was not so clear to outsiders. Japan in this era had a figurehead Emperor and a governing Shogun, but nobody outside Japan knew this well.
I’m skeptical. Consider that in the Constitutional Convention Washington was the presiding President who said nothing substantive from the chair. This was a good encapsulation of the value of having some separation between the formal leader and the functional one. As President, Washington did something related by making Hamilton his practical Prime Minister and remaining aloof. (George W. was good at being aloof.). If the Framers had created dual positions in 1787, you could easily imagine Benjamin Franklin as the first figurehead.
Perhaps Washington’s rectitude convinced people that Presidents would be judicious in their political involvement and preserve their dignity. If so, that was a mistake. Perhaps people thought that the Vice President would be the ceremonial official, which was not an implausible thought.
UPDATE: Franklin was the President of Pennsylvania’s Executive Council from 1785-1788. This was largely a ceremonial role.