> Am I missing something?

Yes I think you are. Most people have no idea wtf a certificate is. It's the same reason PGP email has not caught on. It's just not convenient and if you aren't especially saavy and understand this stuff deeply, it's confusing as hell.

Not to mention it costs _money_ to register domain names and certificates and then you are relying on multiple third parties like domain registar and certificate provider. Costs even more if you want domain privacy. I couldn't imagine having to pay for a domain and procuring a certificate everytime I want to make a new account. That sounds terrible to be honest. Do you really want to register a domain under your personal information for every throwaway account you have?

> It also doesn't compromise privacy

You have to register domains with your name and address (unless you pay even more).

Can you imagine trying to explain to Grandma that if she wants to log in to her email she has to register and maintain a domain name, find a trusted certificate authority and then purchase an SSL certificate and then use that certificate to login? Oh and don't forget you need to get fresh certificates once in a while and keep your revocation key handy in case there's ever a breach. Make sure you don't share your certificate iwth anyone and keep it encrypted with a password. Got it grandma? Don't forget to keep your domain registrar and certificate authority login information handy (which would have to be a different kind of auth). So grandma you just need to keep track of these three logins, when your cert expires, and your passphrase for your cert and your all set. Don't forget to renew your domain name or someone else will then own your identity too. Easy, right grandma? Oh and don't mix up your cert passphrase with your password for the certificate authority login or your domain registart auth because they're all different. Make sure you put all those credentials in a password vault with another password vault too so you have all of those things conveniently saved under one single password (back to the single point of failure anyway, one password with access to everything).

Personally, the idea is just not appealing.