X.509 already does that, and in a better way. It also makes it unnecessary to register multiple devices, if you allow certificate chains (the server would check

X.509 already does that, and in a better way. It also makes it unnecessary to register multiple devices, if you allow certificate chains (the server would check the certificate chain; one of the was issued by the service and contains information about which account it is associated with; the other ones you can issue to yourself, optionally with more restricted permissions, and can be revoked or expire). That would also allow you to have passworded private keys, and/or to store one private key on a separate computer that is not connected to the internet to issue the other one to yourself in order to mitigate security issues (and you can revoke the certificate and make a new one if it is compromised or expires). X.509 also is not limited to only WWW, so it can be used with other protocols too.