“...few of our prominent citizens were natural born citizens...” True, but the Art. II language goes on “or a Citizen of the United States, at the time of the Adoption of this Constitution...” So the Founders were clear as crystal on this requirement, 14 years post founding. They anticipated that their generation would not be around for but a few more elections and were likely biased toward those who were born here and Citizens in 1789. So, for example, Alexander Hamilton was unlikely to be considered as eligible.
“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.