You didn’t finish the analysis of Elk v. Wilkins. The difference between Native Indians and aliens is that Native Indians were located within the borders of the U.S., and aliens were not. Both were subject to foreign jurisdictions; one from a foreign jurisdiction located with the U.S. borders, the other from a foreign jurisdictions located outside the U.S. borders.
You missed the key point of Elk which is that he was born on an Indian Reservation. Indian Reservations were treated as semi sovereign areas which were governed by treaty but not law. Thus he was not born subject to U.S. law which meant that he was not born “subject to the Jurisdiction...” of the United States. It was not decided based on your foreign allegiance idea which was specifically rejected by the Supreme Court in Wong Kim Ark.