Ted Cruz is a naturalized citizen by the statute you mentioned. The constitution gives Congress the authority to make these laws governing citizenship of anyone who is not a natural born citizen. These statutes are changed from time to time. But, Congress cannot change who is a natural born citizen.
Congress has No authority to make a statute governing the citizenship of a person born in the US of Citizen parents; thus, you have never seen them described in the statutes. The statutes describe all others and how they may obtain citizenship at birth or otherwise.
Aliens who wish to become citizens must go through a naturalization process set up by Congress.
Those who are born as citizens are natural born citizens as they have no need of naturalization. Your assertion that “Congress has no authority to make a statute governing the citizenship of a person born in the US...” is demonstratively incorrect.
Firstly, Title 8 section 1401 subsection A clearly describes the situation you speak of and secondly, the very first Congress stated that individuals born beyond the jurisdiction of the US, to US parents where to be treated as “natural born citizens”.