I don’t have time to copy your comments, but I read them. Let me put it this way:
They had to resort to basic natural, international law because each state was its own effective nation, hence called a “state,” under the Articles of Confederation.
And that is what they did.
And natural law stipulates hereditary right by paternity. That is what Vattel and the founders all understood, by nature.
Quibbling with the premise, as if it’s not
relevant or logical, seems to be an exercise
in fantasy and wishful thinking by one who
chooses to ignore the very foundation of its
common sense and fundamental soundness.
They looked at international law and natural law theories. Then they formed their own laws. If they didn't develop "natural born citizen" as distinct from "citizens by birth" or "native-born citizens" it could be a sign that they didn't simply want to rely on Vattel's view as opposed to Blackstone's or some other view.
Whether citizenship requires a native-born father or mother or birth inside the country isn't an essential point of natural law that would override two centuries of a country's legal practices.
It really isn't a question determined by international law theories, as opposed to the laws a country makes for itself. And it isn't a question of human rights that would justify overturning established laws.
From what I've seen of Vattel he presents his theory of how citizenship should be defined and determined, but he admits that different countries do things differently.
Vattel says that in England a foreigners children can be "naturalized" by birth there. One of the commentators says that the children of foreigners resident in Britain would be born citizens, with no "naturalization" necessary.
I can't vouch for the details, but it looks like 1) Vattel's theories don't coincide with the British tradition which is closer to our own, and 2) Vattel would admit that his theories were just that -- what he thought should be, not what was true in various nations of the world.
I agree with the idea that citizenship shouldn't simply be extended to "anchor babies" who just happen to be born here to non-citizen parents who just happen to be passing through. But the notion that a child born here to an American mother is a second class citizen if his father wasn't a citizen is one that no court would accept now.
The Supreme Court addressed this question in the 19th century: there were two kinds of citizens -- native-born (natural-born) and naturalized. In Minor v. Happersett 1874 they acknowledged "doubts" about whether a native born citizen had to be the child of parents born in the country. It was a gray area.
Later on the court stopped acknowledging the "doubts." If you want to reopen the question, go ahead, but what was a gray area then isn't going to be black and white now.