And yet, technologies like HTTPS have now become mainstream, in part due to pressure from big corporations (like Google search rankings), in part due to technologies to make safe defaults easier (Certbot, web servers like Traefik and Caddy). Surely with time authentication and authorization methods will get a similar treatment?
It's unfortunate that following X.509 best practices would involve sharing personal information, instead of putting a UUID in some field that only has a meaning server side, since most private information is already stored on sites in some capacity, for example, to enable payments.
It's good to know that people have made progress with WebAuthn, though, even if roaming authenticators will probably slow down the adoption a bit.
Some reasons:
Initially this doesn't make any sense. Tim's toy hypermedia system (the Web) does not have any of the properties you expect today, it doesn't achieve Confidentiality, nor Integrity, nor Authentication. So it's like you live in a village where they don't have doors yet and you're wondering why there's no locksmith.
Once it did exist the UX for client TLS certificates in browsers is very bad. But of course we could in principle improve that UX.
However an underlying reason is that this approach has lousy privacy properties. Certificates tie an identity to the key, and the Certificate Authority - whoever that would be in this setup - needs to be able to verify those identities or else you aren't Certifying anything. So now maybe you're giving Facebook an X.509 certificate with your full legal name, place of birth, and so on. Most people are not comfortable with that. Even those people who are cool with giving Facebook their real personal details may not be keen to share them also with Google, Twitter, Porn Hub and their favourite web comic.
This is why FIDO tokens used for WebAuthn give a completely fresh random ID and key for each enrollment. Who am I? I'm definitely the exact same person I was when I enrolled here, and more than that I shouldn't need to prove. You can't tie these identifiers and keys to other accounts on other services or even to other accounts on the same service.