The introduction of profile and visibility settings only allows control on restricted fields of managed account profiles such as full name.
All other fields below are not restricted to organisation admin only update , nor is there allowance to make these fields editable by only organisation admin.
This feature request scope is to allow restriction to the update of sensitive fields like Job Title, to be only allowed to Site Admins and Organisation Admins.
A sample scenario :
Organisations may want to prohibit end-users from setting their own information like job
title. Ideally, this will come from trusted sources internally in their organisation instead.