At present users have full control over which of their fields are visible (anyone / members / no access) and indeed can hide their profile completely from everyone else.
In some community sites this is inappropriate as it allows users to enjoy the rights of membership (since they can see other's records) while not taking on the responsibilities of membership (since others can't see their record either at all or enough of it to be useful).
I'd thus like to see the Member Profile Page modified so that in addition to setting default access levels for each field the admin can (where necessary) prevent the member from changing the default setting. (I envisage a fourth column on the table with tick boxes labeled "User Can Edit" or similar)
Members would still be able to see what setting was applied to each field in their own record but some fields might be grayed out where site configuration prevented the member editing the privacy setting for that field.
If a member felt unhappy with the minimum level of responsibility to other members required by the site then they always have the opportunity to leave.