You should 100% make the room code only visible to the host of the room.
To clarify: I think this should be a thing for private games, ESPECIALLY for livestreaming. I've seen it be a problem for a ton of streamers accidentally showing the room code.
uhm... no. I understand that you don't want people who are teaming up or in phone call to join together and ruin the game, but if I'm with a friend and want to play together one of us will join a public room and tell the other the code (we don't talk while playing, we're not assholes) and making a new room everytime and then hoping people join would be pure suffering