“Most citizens were natural born citizens, but the framers wouldn't leave eligibility requirement for the president to Congress”
That is incorrect. Almost all U.S. citizens at that time were citizens at the time of the adoption of the Constitution. They were almost all born as natural born subjects to the Crown of England.
As I see it, along with others, is that the Founders recognized the dilemma of excluding from the POTUSA existing citizens of the colonies. The Founders very knowingly crafted into the Constitution that these existing/living citizens and only these would be exempt from the ‘natural born citizen’ mandate.