Will you and the website owner each verify the key fingerprints? What I'm getting at is it's a hard problem to solve, because users want it to be quick and easy. But that often works against the stated goal of security.
I don't see why the website would need to verify my key fingerprint. Verification is needed when you care who a key comes from. For typical websites, they don't need to know who I am. They only need to know enough to recognize on subsequent logins that I'm the same person who provided the key at account creation, and the key itself has all they need for that.