I agree with pretty much everything you said - but I don’t see how it addresses anything relating to the definition of what a natural born citizen is.
The logic is simple, but results in finding that Wong Kim ark was wrongly decided. Just a quick summary of WKA - the majority stretched the phrase "subject to the jurisdiction" to include aliens temporarily on US soil, except ambassadors and hostile armies.
The logic of applying the preamble is that children of aliens aren't part of "we the people," because they aren't part of "we the people's" children (posterity). The document secure to "we the people" and our posterity, not to the posterity of aliens. Therefore, the posterity of aliens aren't citizens, and if they aren't citizens, they can;t be natural born citizens.