Estonia's PKI is basically identity. Yes, you could build something on top of the public Personal Identification Number, but no reasonable provider accepts that as the username - it is a person using the certificate stored on smartcard/smart SIM(/phone) to identify and authenticate at the same time.

> It seems like a lot people here are confused as to what is an identifier and what is authentication.

I'd say it's you who can't fathom that the two things can work together and only together in some cases.