Founder and Historian David Ramsay Defined Natural Born Citizen in 1789.
Too bad he didn’t post his thoughts IN the Constitution where it would carry weight.
The evidence is clear that Americans at the time of the writing of the Constitution used the term Natural Born Citizens the way it was in the common law, and never used it in the Vattel sense.
Because of the Wong Kim Ark decision every child born in the USA is Natural Born (except for the children of foreign diplomats).
The Declaration of Independence says: We hold these truths to be self-evident, that all men are created equal.
Following that principle, the US born children of foreigners are equal to the US-born children of US citizens. To say that the writers of the Constitution did not really believe it because they really meant that the US-born children of foreigners could not be president while the US-born children of US citizens can insults the framers and makes equality a lie.
It is possible that some of the writers of the Constitution thought that, BUT NONE OF THEM SAID IT.
If there had been letters or articles saying that the Americans at the time feared the US-born children of foreigners, there would be a reason for thinking that the writers of the Declaration were hypocrites when they wrote that all men were created equal. To be sure, some of them did not believe that slaves were equal to freemen. But it is unfair to our founders to assume prejudices that there are no evidence for. Only if they actually said we believe that the US-born children of foreigners are not equal to the US-born children of US citizens is it fair to them to believe that they thought it. AND THEY DID NOT SAY IT.