John Bingham, primary author of the 14th Amendment, was concerned, PRIMARILY, with crafting an Amendment that would overturn the Dred Scott decision.
The 14th Amendment is an INCLUSIVE Amendment. It was not the role or the desire to EXCLUDE anyone, from Citizenship, with that Amendment.
Congress clearly has the right, under the Constitution and under all Amendments, to establish the rules for Citizenship, within Constitutional guidelines.
The application for a Passport makes clear that there are two basic ways to gain citizenship: Birth or Naturalization.
If you ARE a Citizen, and you were NOT Naturalized, chances are high that you are a Natural Born Citizen. There are only a few exceptions to this rule.
Take a grape and define it as sweet tasting with a green skin and seeds inside. Just because an "orange interior" was not excluded does not permit that a papaya is also a grape. It only means that the grape requires further definition.
Your "inclusive" and "exclusive" argument only emphasizes the need for the legislative and legal systems to further define "natural born". Until such occurs, in my opinion (humble as it is), we have to use the definitions that are historically provided such as they are.
Jurisdiction-in-birth and allegiance-in-birth are referenced in several documents as being prerequisite to the "natural born" status. There are no other definitions at this time -- so that's the grape we're left with for the time being.
I am sincerely in support of defining this grape further. But until then, from the historical and Constitutional point of view available to me, papayas are not now, nor have they ever been, grapes.