If you’re on Hubzilla or (streams), and you’ve grokked it enough to use it accordingly, then you can actually post content in private to only selected users.
As an administrator, the only time you would want to turn on the public stream is if you are a public hub and accept new signups. It makes it easier for administrators and moderators to moderate the public content on their own server since they can see all public posts in one place. If someone is posting illegal content or spam, a moderator can see it, and remove it (and perhaps the user too).