I was just looking for a way to disable the ability of users to enable/disable their email address in their profiles and came upon this thread (http://moodle.org/mod/forum/discuss.php?d=131099) . It appears it's not currently possible as the only options are to:
-prevent them from enabling/disabling *other users'* email addresses (Enable/disable email address moodle/course:useremail))
-prevent them from editing their own profile entirely. (moodle/user:editownprofile)
It would be great to bring a new "Profiles" section into the Roles and Capabilities for each user definition, and then break it out to the various items within the profile: picture, email enable/disable, password, interests field, etc... so that it would be possible to allow or disallow each item separately.