All children born abroad must have paperwork filed for their citizenship to be recognized by the US government.
Natural born citizens need no action of law.
They are naturally citizens because there is no other possibility.
You're using the same logic used by those that argue our second amendment rights are granted by the Constitution. They are not. They are granted by God, and formally documented by the Constitution. A Consular Report of Birth Abroad does not grant citizenship, it recognizes and formally documents the citizenship of a citizen whose status as natural born is inherent in his/her birth to two American citizens. A child born today in Kansas to an American mom and dad doesn't become a citizen when the birth certificate is issued. He is a citizen at birth, even if it takes a little while for the paperwork to catch up.