The Supreme Court has never held a case specifically about the children of illegal immigrants. However, the Supreme Court did have a case where it determined that a child born to a foreign immigrant in the U.S. was a citizen (United States v. Wong Kim Ark, 169 U.S. 649 (1898)).
In Wong Kim Ark, a Chinese laborer was brought over to help build a western railroad, had a child, and then returned to china. The child later wanted to return to the U.S. claiming that he was a citizen but the U.S. congress had recently passed the Chinese exclusion act and tried to keep him out claiming that he was not a U.S. citizen since he had been born to a foreigner. The Supreme Court ruled based on the 14th Amendment that he was a citizen because (1) He was born in the U.S. and (2) His father had been subject to the jurisdiction of the U.S. because he had been subject to the laws of the United States while he lived in the United States unlike a diplomat who has diplomatic immunity from U.S. law.
Most of what you said is correct but there are a few other facts. Wong Kim Ark’s parents had returned to China and he made two visits to China to visit them. When he returned the first time, he was allowed back in to the U.S. and deemed to be a “native.” On his return from trip number two in 1895, he was detained and labeled a foreigner. He sued and eventually the Supreme Court ruled in his favor 6-2 thus establishing birthright citizenship under the 14th Amendment.
From the Court’s ruling:
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’ 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.”
BUT, the parents were here LEGALLY. Quit trying to obfuscate the whole story. Anchor Babies is an issue because of ILLEGALS.
FN 10 in Plyler v. Doe, 457 U.S. 202 (1982)
Agreed it's not literally a holding. Excerpt from FN 10 ...
As one early commentator noted, given the historical emphasis on geographic territoriality, bounded only, if at all, by principles of sovereignty and allegiance, no plausible distinction with respect to Fourteenth Amendment "jurisdiction" can be drawn between resident aliens whose entry into the United States was lawful, and resident aliens whose entry was unlawful.