Six Justices of the Supreme Court disagreed with your point of view in 1898 and for the last 117 years, their opinion has held sway:
United States v. Wong Kim Ark (1898)
[An alien parent’s] allegiance to the United States is direct and immediate, and, although but local and temporary, continuing only so long as he remains within our territory, is yet, in the words of Lord Coke in Calvin’s Case, ’strong enough to make a natural subject, for, if he hath issue here, that issue is a natural-born subject’.
“Subject’ and ‘citizen’ are, in a degree, convertible terms as applied to natives; and though the term ‘citizen’ seems to be appropriate to republican freemen, yet we are, equally with the inhabitants of all other countries, ’subjects,’ for we are equally bound by allegiance and subjection to the government and law of the land.’
“…every child born in England of alien parents was a natural-born subject, unless the child of an ambassador or other diplomatic agent of a foreign state, or of an alien enemy in hostile occupation of the place where the child was born.
The same rule was in force in all the English colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the constitution as originally established.”
Some people born in the U.S. are citizens by law and some people born in the U.S. are not citizens by law. If birthplace cannot determine citizenship, how can it determine natural born status?
And those same six, plus another one, agreed that Blacks are second class citizens. (Plessy v Ferguson.) I'm thinking their judgement is faulty, so we ought not trust it.