Is SSH public key authentication weakened by 'none' cipher?
It is critical to combine both the key exchange and the secure channel, otherwise someone can mount a man-in-the-middle attack.

The way we prevent a man-in-the-middle attack is to do a key exchange, to exchange a session key that both endpoints know but no one else (including the man-in-the-middle) can know, and then authenticate both endpoints.  You seem to suggest that we remove the encryption, remove the secure channel, don't bother negotiating a session key.  If we did that, then the protocol would become vulnerable to man-in-the-middle attacks (active attacks), because nothing binds the signature/authentication phase to the rest of the stuff sent over the SSH channel.