Update: today I found a way of hiding certain featured collections for specific user groups.
In the user group permissions for the group of non logged-in users, I have now disabled viewing all collections apart from one that is aimed at the non logged-in users.
The others are off limits to them, and require one to log in before they even see the folders and folder structure.
It's still not possible to totally hide the featured collections link from the menu, but since the public user will still find some content in there, it's actually OK.