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I'm addressing what I perceive to be your misunderstanding that the legal concept of "jurisdiction" only applies to a person after the relevant jurisdictional body has notice of a person's presence within its boundaries.

I don't like the legal concept of citizenship by place of birth.

U.S. v. Wong Kim Ark, 169 U.S. 649 (1898) discusses, among other things, British common law that all persons born within the British realm, unless the child of a foreign minister, ambassador, or alien enemy during and within their hostile occupation of part of the King's dominion, are citizens of the King.

Wong Kim Ark is worth reading, even though I consider it bad policy.

In Wong Kim Ark, the Court says:

In construing any act of legislation, whether a statute enacted by the legislature or a constitution established by the people as the supreme law of the land, regard is to be had not only to all parts of the act itself, and of any former act of the same lawmaking power of which the act in question is an amendment, but also to the condition and to the history of the law as previously existing.

Wong Kim Ark at 653-654.

The Court later says:

It thus clearly appears that, by the law of England for the last three centuries, beginning before the settlement of this country and continuing to the present day, aliens, while residing in the dominions possessed by the Crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, the jurisdiction of the English Sovereign, and therefore 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.

Wong Kim Ark at 657.

That's simplistic, and certainly not all Wong Kim Ark discusses, but those two paragraphs say a lot about the Supreme Court's view on U.S. citizenship of most babies born on U.S. soil.

I take not that Wong Kim Ark's parents were not illegal aliens, so that issue is not specifically discussed. However, the opinion does not say it is limited to children of legal resident aliens in the U.S.

As I said, I don't like the public policy.