To the OP:
Your reasoning is sound based on the society, thoughts and intentions of the framers of America and it's Constitution.
The problem is, over the last 60 years or so, a large contingent of Americans cannot and do not identify with the society, thoughts and intentions of the framers because they are not like them.
A large and growing number of Americans are anti-God, anti-human, pro-godless government, pro- "mother earth". These people have NOTHING in common with the people who began the USA and framed the Constitution that guides it.
Since they cannot or will not understand or agree with the highly religious founders of America, they want to live in opposition to the Constitution as well as the God who created them.
The only people who care about the Constitution and all it's explicit references to the Creator are those who are like-minded with the framers of the USA and it's Constitution - BELIEVING/PRACTICING CHRISTIANS.
Sorry, this is revisionist history. Yes, there were framers that were religious but there were just as many that were not. George Washington, according to his pastor, rarely went to church (much like modern day Americans). Benjamin Franklin was agnostic at the time the country was founded.
And most importantly, to the OP, Thomas Jefferson was not Christian -- he did not believe that Jesus was God. He liked many of the stories of the Bible and felt Jesus was a great teacher -- to that end he created his own version of the Bible where he removed any reference to the miracles of Jesus, as well as any references to Jesus' divinity.
As such, "Nature's God" as it appears in the Declaration of Independence is not Jesus/the Christian God. It is part of the reason it is left as "Nature's God", an ambiguous term that is religiously neutral. Further, there are zero references to God in the Constitution.
As far as "Natural Born Citizen", that was a political concept that was well known at the time of the writing of the Constitution. There are two main theories of "natural born" that we know were operative at the time of the writing of the Constitution. One was the English Common law definition, which basically is the same as the current US interpretation where any child born in the country is "natural born" -- as opposed to naturalized. And I must point out, to create the original US laws, the Founders basically "borrowed" English Common law -- so there is a strong reason to care about the English common law definition of "natural born citizen". The other theory was that of Vattel, who more or less agreed with Pennmark, that the father must be a citizen.
The truth is, however, neither side could ever convince the other. Based on the fact that the Constitution does not define which of the two theories (or some other idea of natural born the Founders believed in) indicates that neither side was able to convince enough people to get their theory added to the Constitution. Instead, they left it ambiguous and undefined. We have no actual evidence of what the Founders, as a group, intended (though plenty of evidence about what some individual Founders believed).
Because there is no "mandate" on this issue, the Supreme Court and US law have been the driving factors on what determines a "Natural Born Citizen". And current US law, as well as current Supreme Court precedent, set up "natural born citizenship" by birth in the US or birth to a single parent that is a US citizen.
I understand many of you don't like this but this is current US law. If you don't like it, feel free to petition Congress to change US law and/or to pass a Constitutional Amendment to define "Natural Born Citizen" more to your liking. Beyond that, your opinion of how "natural born citizen" should be defined doesn't matter since it is currently defined by law.
