And that is where you are going wrong. The authority is NOT "power to naturalize" the authority is "To establish an uniform Rule of Naturalization". That is FAR MORE than just the power to naturalize.
The rule of naturalization includes:
Rules that govern who is able to be naturalized
Rules that govern who can never be naturalized
Rules about how to apply for naturalization
Rules on how citizens give up their citizenship
Rules on the process and procedures on how an alien becomes naturalized
Rules on who does not need to be naturalized
Rules on who is a citizen at birth by the circumstances of their birth (naturally born a citizen)
And assuming for the sake of argument that Congress has the power to declare aliens to be naturally born citizens, none of that is a limitation on establishing rules on who is a citizen at birth by the circumstances of their birth.
You said, in the first place, "There is NO LIMIT ON THIS AUTHORITY other than Article 4 Section 2 and the 14th Amendment." I asserted that Art IV Sec 2 and the 14th amendment do not limit the power to establish an uniform Rule of Naturalization.
Your list has some other errors, but that's okay with me.