Such agency can force PM to modify login process to derive password from submitted form, or to just switch private keys for non-encrypred ones, because the user won't even notice it.
Truly secure entity just wouldn't have private keys on a server at all. Users would have to go through an an uncomfortable process of generating and uploading keys to clients, but they would be truly safe.
To sum it up, you can't really have security and convenience at once. besides skipping a proper key management process, PM also mail skips such important steps as verification of email partner identify and key verification, so you have to trust PM that you are really talking to a person you think you are talking.