As I understand it, the US presidential model is defined as an "executive" one and is partisan. It is not the only model available. There can also be a non-partisan head of state, such as is found in Ireland.
America rejected the rule of the British and its monarchy. Who exactly could have taken on the role of monarch? Or is it suggested that their bid for independence was a retrograde step and that they would be better off being ruled by a monarch situated several thousand miles away? Our monarch continues to be sovereign over 15 countries, also situated many thousands of miles away. Is that a desirable situation?