Illegal aliens are subject to US jurisdiction. The only recognized exceptions are for children of diplomats/foreign leaders born here, children of enemy combatants, and the antiquated Native American exception (which has since been eliminated by the passing of The Indian Citizenship Act of 1924).
Briefly, birthright citizenship goes deep back into medieval English common law. Most cited, that I've seen, is Calvin's Case. The controversy involved a person born in Scotland shortly after the English throne descended to Scottish King James VI. The case addressed whether persons born in Scotland, following the descent of the English crown to the King James VI, would be considered "subjects" in England.
In short, the case held that that all persons born within any territory held by the King of England were to enjoy the benefits of English law as subjects of the King. A person born within the King's dominion owed allegiance to the sovereign and in turn was entitled to the King's protection.
The case is so antiquated and steeped in intricate matters involving the formerly separate kingdoms of Scotland and England that it's a bitch to read. Here's the case if you're interested in hours of masochistic reading:
https://www.constitution.org/coke/Calvins_Case-7_Coke_Report_1a_77_ER_377.html
Here's a lengthy Yale Journal piece summarizing Calvin's Case and explaining its significance:
https://digitalcommons.law.yale.edu/cgi/viewcontent.cgi?article=1170&context=yjlh
There's absolutely no way a majority of the SCOTUS would rule against birthright citizenship. Thomas, Alito and Gorsuch love themselves some English Common law. No way they contort themselves into ruling against it.