Why not the CRBA?
Why are CRBAs not open to the public? Or why didn't Cruz produce one?
CRBA's are not open to the public for a similar reason that birth certificates aren't. A person could snag one and represent himself as that person.
I have no idea if Cruz has either a CRBA or a Certificate of Citizep, or even a US Passport. I've read that he traveled on a US Passport while in high school. Lack of production could be due to not having one, or not thinking it was necessary to make the argument, or maybe to allow tension to build over the issue. All I have on that question is speculation.