There'd need to be some central authority (like you said) doing the certificate issuing that verifies that you are, indeed, a human, and that your a unique human that they haven't already given a certificate to.

Chances are they'd want more than a phone number; probably a photo ID or something as well, else their value proposition isn't very strong.

I'm not sure if that's better for privacy and safety than many services asking for just a phone number (which I can generate a semi-throwaway Google Voice number for).