If you use the "Create chat room with user" feature. Why are there no options to make the chat private, but there are options to add read only users for rooms that are private?
Almost everything you do on StackExchange is public. This is intentional; as moderator Marc Gravell points out in this post: "Bad things happen in the dark".
Only moderators have some options to contact people privately.
Because ideally anything you're chatting about should be site related, and should include helpful information when other people are faced with same problem.
Essentially it is an extension of the Q&A system to handle situations where real-time communication is needed to better clarify communication and not flood the comment areas (which are there to clarify information). If comments are to clarify answers, chat is to clarify comments.
Good uses for chat include: coming to a consensus, clarifying comments, real-time chat needed for clarity, (politely) resolving misunderstandings.
Chat is not technically there for idle chat, but that is not strictly enforced.
Private chat rooms for lay-users would encourage idle chat, and likely hide useful information for future users.