make it mandatory for all US presidents to place the left hand on the US Constitution while taking the Oath of Office.

The Oath of Office is very clear: "I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the CONSTITUTION of the United States."

The United States presidents to not swear to preserve, protect and defend the Bible, the Quran, the Torah or any other religious book.