This would be more for support posts or report posts.
Let’s say there’s a support section. You want to post a support request, but you don’t want the world to see your private info, or if it’s a report – you don’t want to stir up drama by showing A reported B.
I’ve seen this before in old phpbb long ago and it works well:
Have an extra set of permissions to allow to create / see / create (self only). You could only see your own posts. Then normally in my demo situation, you’d add a 2nd (existing) permission for create / see / create (all)
EDIT: It would probably be more clear and consistent to name them:
Create / Reply / See (All)
Create / Reply / See (Self)