Perhaps I am wrong, I don't have any children, but my understanding is that birth certificates are identifying documents. As such, sex is a useful identifying characteristic, especially for a baby, which is when a birth certificate is issued. So I think it is a reasonable piece of information.
I'm not sure what you are asking about, though. Are you why sex is a good piece of identifying information?
I'm asking why you think the birth certificate is a good or necessary identifying document
for purposes of identifying sex?
I do have a daughter, and 3 step-sons. Yes, throughout their early childhood I was required to produce their birth certificates to verify age and U.S. citizenship... typically for school enrollment.
In no situation did I need to produce a birth certificate to prove their sex.
The only people I know who think birth certificates are necessary to specifically prove sex are the religious freaks in the U.S. would like to see that happen in order for school children to use a bathroom or to find shelter from an active rampage shooter.
So I'm still trying to find an actual VALID reason to indicate sex on a birth certificate.
Ironically, it was my daughter's hospital certificate of birth (not the official government issued birth certificate) that had what I think was a much more important identifying piece of information - her footprints.