Too many public keys

[Andy Lutomirski]

Apparently my ssh agent is feeling energetic today:

debug1: Authentications that can continue: publickey,password
debug1: Next authentication method: publickey
debug1: Offering RSA public key: [...]
debug1: Authentications that can continue: publickey,password
debug1: Offering RSA public key: [...]
debug1: Authentications that can continue: publickey,password
debug1: Offering RSA public key: [...]
debug1: Authentications that can continue: publickey,password
debug1: Offering RSA public key: [...]
debug1: Authentications that can continue: publickey,password
debug1: Offering RSA public key: [...]
debug1: Authentications that can continue: publickey,password
debug1: Offering RSA public key: [... (this is the only remotely sensible try)]
Received disconnect from [a.b.c.d]: 2: Too many authentication
failures for [username]

The client is 6.1p1 and the server is 5.9p1.

The web is full of workarounds (IdentitiesOnly, SSH_AUTH_SOCK=, etc),
but I think this is silly.  This IMO shouldn't happen and, if it does,
the error message should give a better clue of what's wrong.

--Andy