I’m sure the framers were concerned about naturalized citizens as well.
We know they were, because they mentioned Naturalization in Article I Section 8 Clause 4.
Naturalized citizens become We The People after they are naturalized, and then once naturalized, but not before, their posterity are citizen children.
If resident aliens have children here before they become naturalized, then those children's (who are dual citizens who claim birthright in the United States but also inherit the citizenship of their parents) children will become natural born citizens, but they themselves will not.
That's why I think that the SCOTUS was wrong in Minor v. Happersett when they said they had to look elsewhere for the definition of "natural born citizen." That definition is right there in the Preamble as I've just shown.
The Preamble sets the context of the rest of the Constitution, namely to preserve the country for its citizens and their citizen children.
-PJ
Positive law, not natural law.