Your identity provider doesn't need to be your email provider. You can use something like https://www.persowna.net/ (disclaimer: I wrote it), which can use any manner of authentication it likes. I may just add client SSL certificates as a way of authentication, that will be interesting.

You can also self-host and choose any authentication you want, however specific to you.

Also, this isn't directly relevant to what the GP said, but using a standardized, decentralized way to authenticate is a huge win. It effectively turns all sites into requiring arbitrarily strong authentication (at the very least, everything suddenly supports two-factor auth when it supports Persona), but you still don't have to trust a third party with your authentication (you can run it on your home computer).

It's Personas all the way down... ?