“If birth here was the sole criteria, none of these people would have ever been excluded from citizenship.”
You misread the post. I did not say, nor evern imply, birth was the sole criteria.
There is a material difference between children of diplomats, for example (who are not citizens, even now) and children of persons who have have consented to pay taxes and submit themsleves to the laws of the USA (such as resident aliens).
Children of legally resident aliens are natual born citizens.
There are two schools of thought on this of which I am aware. There are those that Hold Wong Kim Ark is correct, and that it was the intent of the Congress and the 3/4ths of state legislatures that anyone born to a legal resident can claim U.S. Citizenship. (Note, not the same thing as "natural citizenship.)
There are those who claim Wong Kim Ark was decided incorrectly, and that it's decision is in actual contradiction with the meaning and intent of the 14th Amendment. This group holds that The Congress did not intend to create an amendment that gives citizenship to the children of foreign transients. (Anchor Babies.)
In either case, regardless of whatever interpretation of Wong Kim Ark and the 14th Amendment is used, none of these interpretations claim that citizens by action of the 14th Amendment are "natural citizens."
The Constitution does not, in words, say who shall be natural-born citizens.
If the 14th amendment created "natural citizens" the Waite court would not say the constitution was silent on the issue, it would say "Oh Yes it does!"
I do not think most people understand the significance of this. The Court in 1875 would have had a far better understanding of what "natural born citizen" meant than would later subsequent courts, and yet fresh off the creation of the 14th amendment it could not find one there. It had to resort to a different standard.
Resort must be had elsewhere to ascertain that. At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners.
The Fact that the Waite court did not and could not find "natural citizen" in the 14th amendment, indicates that the Gray Court did not find such a thing in there either, but people have ever since misapplied the ruling of "citizen" to mean the same thing as "natural born citizen."