The passphrase that can be set on the private key is unrelated to the SSH server or the connection to it. Setting a passphrase to the private key is merely a security measure the key owner may take in order to prevent access to his remote shell by a third party in case the private key gets stolen.
Unfortunately, you cannot force users to secure their private keys with passphrases. Sometimes, unprotected private keys are required in order to automate access to the remote SSH server. One good habit I highly recommend for such cases is to advise the users to hash the known_hosts file (stored at ~/.ssh/known_hosts), which keeps information about the remote hosts the user connects to, using the following command:
ssh-keygen -H -f ~/.ssh/known_hosts
This way, even if a third party gained access to an unprotected private key, it would be extremely difficult to find out for which remote hosts this key is valid. Of course, clearing the shell history is mandatory for this technique to be of any value.
Also, another thing you should always bear in mind, is not allow root to login remotely by adding the following in your SSH server's configuration (sshd_config):
On the other hand, if you want to prevent users from using keys to authenticate, but instead use passwords, you should add the following to your sshd_config: