You still miss the point. The constitutional authority of Congress to set rules for naturalization has nothing whatsoever to do with the intention behind the selection of the words “natural born citizen” in the presidential eligibility clause of Article II of the Constitution. Have you ever had to brief or argue a constitutional question in a court on this point? Have you ever dealt with naturalization before a forum as opposed to interpreting language in the Constitution? They are two entirely different things.
You are still missing the point of Article 1 Section 8. There is NO LIMIT ON THIS AUTHORITY other than Article 4 Section 2 and the 14th Amendment which was pass long after the founders wrote the Constitution.
If you believe other wise, then show via the Constitution where this authority is limited.