This has now been in use and tested on a number of live sites.
The 7.x-1.0 release adds a new PERMISSION that restricts access to the Advancedform toggle.
Add "Use Advancedform" as a permission in /admin/people/permissions
If a user does not have the permission, the advanced fields will still be hidden, but they will not have the ability to 'unhide' them with the on-screen toggle.
Again, this is not security, and can be thwarted by a client-side javascript hacker, but will reduce screen clutter without getting into full 'field permissions' etc.