I can see this being useful if you have lots of keys and the server kicks you when you try too many of them, but in theory you really shouldn't need more than one key.
No, that's a little different. The problem with password reuse is that if someone breaks into a site and steals the passwords, or a malicious administrator steals your password, they can reuse it. The public/private key separation of ssh keys means that that is much less of an issue. You can't login to another server with my public key.
If the integrity of a password was dependent on a one-time unlocking mechanism secured on my local machine, then yes, you would only need one password. Passwords are not public key cryptography.