The operative word is citizen. Section one grants citizenship to anyone born in this country that is under our jurisdiction. It is not limited to slaves.
‘Subject to the jurisdiction thereof’ means owing no other allegiance than the U.S. (stateless slaves)
Why would the authors of the 14th want to naturalize whole swaths of foreigners, illegals, etc for perpetuity under an Amendment when the Congress has the power to naturalize?
That’s right, they wouldn’t.