It would accomplish just what the commie Democrats want, what the commie RINOs want, and apparently what you want.
No amount of paper is going to "prove" that either Obama, Rubio, or Jindal are Natural Born Citizens, because neither of them are, and this fact is already known about all three.
None of the three were "born in the country to parents who were both themselves citizens at the time of birth".
Neither are anchor babies. Neither are the half-alien children of someone who took a foreign spouse, and who were born while one parent was not a US citizen. Neither are people who have dual citizenship with any other nation in the world.
Shred the US Constitution a little at a time, and it will mean less and less. Ignore this clause; usurp that one; twist this or that piece out of shape in the courts and public opinion; eventually you will have rendered it totally meaningless and useless as a blueprint for the structure of US government.
So here we are already. The US government, as a union of the several states, exists only as a contract between the states and between the people of those states. Destroy that contract, and the USA is only a figment of the imagination of the thugs who will insist on holding it together at the force of gunpoint.