The founders language is from another time but if you read their writings their meaning is clear.
If they meant anyone born here is a citizen, then that’s what they would have written, and left it at the.
But they added a specific clause “AND SUBJECT TO THE JURIDICTIONS...”
Someone who breaks our laws to get here is subject to another country
They didn't mean anyone born here is a citizen, but the addition of "and subject to the jurisdiction thereof" was to exclude only a narrow set of exceptions -- the two exception known under the common law, plus the additional special case of Indians. The U.S. Supreme Court has explained this:
"The real object of the Fourteenth Amendment of the Constitution, in qualifying the words, "All persons born in the United States" by the addition "and subject to the jurisdiction thereof," would appear to have been to exclude, by the fewest and fittest words (besides children of members of the Indian tribes, standing in a peculiar relation to the National Government, unknown to the common law,), the two classes of cases -- children born of alien enemies in hostile occupation and children of diplomatic representatives of a foreign State -- both of which, as has already been shown, by the law of England and by our own law from the time of the first settlement of the English colonies in America, had been recognized exceptions to the fundamental rule of citizenship by birth within the country. Calvin's Case, 7 Rep. 1, 18b; Cockburn on Nationality, 7; Dicey Conflict of Laws, 177; Inglis v. Sailors' Snug Harbor, 3 Pet. 99, 155; 2 Kent Com. 39, 42." U.S. v. Wong Kim Ark (1898)
Someone who breaks our laws to get here is subject to another country.
Someone who breaks our laws can still be arrested, prosecuted, and incarcerated. That's true for both legal and illegal immigrants. Deportation isn't the only option. Legal aliens still have an allegiance to the country of their nationality and in most cases likely are subject to the laws of that other nation. Yet we recognize that they are "subject to the jurisdiction" of the U.S. while they are here and that children born to them in the U.S. are U.S. citizens.
It is most difficult articulate a meaning and theory of "subject to the jurisdiction thereof" that applies to legal aliens while excluding illegals. Conversely, it is difficult to articulate a meaning and theory of that phrase that excludes illegals that doesn't then exclude legal aliens by the same principle.