Not a rhetorical question: couldn't the malicious server relay the challenge from a valid server for to you to sign, and impersonate you that way?
The man in the middle can still perform denial of service, by dropping some or all of the traffic.
The man in the middle could substitute their own public key in place of one of the endpoint's public keys, but if each endpoint knows the other endpoint's key and is expecting that other key, then an unexpected substitute key will raise a red flag.
If I am a server and have your public key in an authorized_keys file, I can just encrypt a random session key using that and only you will be able to decrypt it to finish setting up the session.
This is why passwords and asymmetric crypto are worlds apart in security guarantees.