Make private group pages visible to only group members

Depends, I suppose, on whether you want to all/prevent other group members from knowing which other members are in the group, or make it an option - I can see use cases for

  1. Non-group members don’t know who’s part of the group, but group members know who are other group members
  2. Non-group members don’t know who’s part of the group, neither do the other group members.

Seems the current situation is slanted towards #2.

Can’t you simply create a category that’s read/write/create only to those groups members? (That will hide them from non-group members, but allow members within the group to at least communicate with each other.)