The wording of the act itself:
All persons born or naturalized in the United States
I reject your definition. "Naturalization" is any law or process created by congress to make citizens out of people who would not otherwise be citizens.
There are born citizens and naturalized citizens.
There are "naturalized at birth" citizens, such as those created by acts of congress which naturalize people at birth.
This phenomena is specifically mentioned in Wong Kim Ark.
" A person born out of the jurisdiction of the United States can only become a citizen by being naturalized, either by treaty, as in the case of the annexation of foreign territory, or by authority of congress, exercised either by declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens, or by n abling foreigners individually to become citizens by proceedings in the judicial tribunals, as in the ordinary provisions of the naturalization acts."
A born citizen doesn't then have to become a naturalized citizen.
When Congress sets the naturalization to occur "at birth", these people are born naturalized citizens.
All persons born or naturalized in the United States
Designating all the persons "born" in the United States identifies who is being naturalized by the act. "Or Naturalized" is already covered by acts of congress naturalizing them.
Congress cannot create natural citizens. Their only power is to naturalize people.