Re: No privacy for the public
I think the original way round is correct - for example it would allow you to provoke someone in what they think is a group message but is actually private. When they reply with abuse to you, it looks like to the rest of the group as if it's come out of the blue.
Or possibly, ask them to share information with the group that they shouldn't so they get the blame instead of you.
All of these require you to be a member of the group in the first place though, as far as I can see. If you invite the FBI into your group chat, you've really only got yourself to blame.