Without a US issued birth certificate you are not a US citizen by birth, the CRBA is the equivalent of a US birth certificate for US citizen born abroad. Where is it?
This might be angels on the head of a pin, but I say citizenship exists independently of certification. Not as common today as in years gone by, but some people born in the US, to US citizen parents, don't get birth cerificates. They are still citizens.
I agree that a CRBA serves the same purpose for citizenship determination, and there is also a Certificate of Citizeship which can be obtained by a person who doesn't have a CRBA but meets the stautory criteria for citizenship.