Profile field sets and fields should be visible to the user at all times so he knows that there is something to fill in and to complete his profile. At the moment the only way the user knows that there are additional fields to fill in is to look at the profile completion widget (when used) or to click the edit button for the mandatory fields and find the hidden additional field sets there. This is more of a detective work and completely against the idea that a user should get encouraged to complete his profile. That only completed fields are shown to other users should not be changed in my opinion but the user itself should see all the fields all the time.