BuddyPress.org

I’m wondering if the remove_cap() method is what you need. Try adding this to functions.php. Feel free to remove it after you’ve visited the front end of your site, it just needs to be run once.

add_action( 'init', function() {
    $role = get_role( 'subscriber' );
    $role->remove_cap( 'upload_files' );
} );

You can do the same with the author and editor roles should you wish.