If the 14th amendment did ANYTHING to create eligibility for someone simply on the basis of place of birth, then the equal protection clause would create that same right for persons who are naturalized. That’s the whole point of the equal protection clause ... EQUAL protection. The court can’t arbitrarily decide one class of citizens has special rights unless that class of citizen has citizenship that is defined outside of the 14th amendment. And that’s exactly what the Supreme Court did in Minor v. Happersett, citing a class of citizenship defined outside of the 14th amendment ... a class of citizenship due to birth to citizen parents and ... and a class of citizenship characterized exclusively as “natives, or natural born citizens” .... and this is what the court later affirmed in U.S. v. Wong Kim Ark, Ex Parte Lockwood and Luria v. United States. Wong Kim Ark said it eloquently — when construing the 14th amendment, the Constitution does NOT say who shall be natural-born citizens. IOW, it’s not enough to be born on U.S. soil subject to the jurisdiction thereof to be a natural-born citizen. There’s no direct evidence to show that today’s Supreme Court would overturn the unanimous precedent of those decisions ... although they might try their hardest to avoid hearing any case that would put them in such a position.
Nothing in the 14th Amendment about Naturalized Citizens; I don't see any argument that Equal Protection has anything to do with the issue.
14th Amendment is a pure place of birth proposition--it says if you are born here, you get all of the rights of a citizen; no distinction about the class of rights.
My own view is that the 14th Amendment did nothing to modify the Natural Born Citizenship definition with respect to such persons (born in the US); there certainly isn't any doubt that the Supreme Court would have held such persons eligible under Article II without regard to the citizenship or place of birth of their parents without the Amendment.
However in 1963, many Conservative lawyers (there were still some around in that era) argued that whatever doubt there might have been about Goldwater's eligibility (because he was born in Arizona prior to statehood) had been resolved by the 14th Amendment because place of birth was always about sovereign jurisdiction and the territory had always been under US jurisdiction.