The big question is what kind of problem is being solved?
Truth is, nobody is giving up good old passwords just yet. Two-factor helps when necessary, but the password is still there.
The actual issue, IMO, is avoiding recovery of the plaintext passwords en masse when a typical website gets hacked. People reuse their passwords. So, as a webmaster, I don't want to be sitting on a pile of weak hashes, etc, etc.
Salted hashes like bcrypt seem to help (as far as I've read about these things). PKI offers even more potential.
E.g. a password-encrypted random keypair could be something - the client gets it at will from the server, decrypts it by prompting for password, and then uses it to authenticate a random nonce from the server.
Effectively, in that situation the server willingly gives up the entire authentication database, but trusts keypair blob's encryption to do its job against brute-force attacks.