The only problem with this, is that it requires everyone to trust a single third party with the authentication. Since the input space that you type in is small, any one-way encryption is easily reversible. This means for every site that the code is good for, you would need to reveal a means to generate the code, rendering it the password problem all over again.

Alternatively, the key-fob could have an arrow to select which site to show the key for, but that would be cumbersome. Personally, I think that a solution similar to the ssh one would be best in that you have some sort of pass phrase that you type into your browser, and it unlocks a private key that can prove your credentials on web sites.