From WKA:
“The question presented by the record is whether a child born in the United States, of parents of Chinese descent, who, at the time of his birth, are subjects of the Emperor of China, but have a permanent domicil and residence in the United States, and are there carrying on business, and are not employed in any diplomatic or official capacity under the Emperor of China, becomes at the time of his birth a citizen of the United States by virtue of the first clause of the Fourteenth Amendment of the Constitution,
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.”
They decided that Wong Kim was a US citizen.
Smith V Alabama is about regulations imposed on Railway engineers.
None of these cases was about the unique issue of Article II Presidential eligibility, i.e. is Obama a Natural born citizen.
Article II does not require only “US Citizen” status, it requires Natural born citizen status. Cutting text from cases that do not address the key issue does not help. English common law does not define "Natural born citizen," and saying "Natural born subject" is the same does not help, because Natural born subject status is the same as citizen. The framers didn't use only the word Citizen in article II.
WKA discusses at length the meaning of natural born citizen. While not binding, it is the only formal discussion by the Supreme Court on the meaning. It was also completely in line with other court decisions that preceded it.
The idea that the US Supreme Court would overturn that discussion, rejecting it completely so as to remove a sitting President, elected by a majority of the people with the full consent of Congress, is absurd.
“So you don’t believe de Vattel was commonly held as a subject-matter-expert...”
Not on citizenship. You will note that your citizenship, unlike Vattel’s writings, does NOT depend on your parents being citizens. You are asked for a birth certificate, not a genealogy.