And??? The CRBA does not make one a citizen - it just records the event, like a birth certificate. Someone born in the US that is not issued a birth certificate is still a citizen. Someone born outside the US to a US citizen is still a citizen even if the CRBA is not filed. The filing just makes it easier to prove that fact.
As a practical matter, one has to have documentation proving citizenship to do things like enroll in school or be issued documents such as a Texas Driver’s License. It is not enough to say you are a citizen and your birthday is X. You have to provide proof, which is what the CRBA or US passport does. I had to produce my CRBA to join the military and get my US passport. I had to show my passport and my wife had to show her Green Card the first time we got Texas Drivers Licenses. I assume Cruz had a Texas DL and a US passport. He should have had to provide either a US passport, CRBA or a Certificate of Citizenship to get those documents.