I've just been in a chat without the ability to speak, and I'm under the impression that not even the owner could see my messages. Given that SO in general doesn't have a private messaging system, it would be useful if owners and administrators could see chats from those not authorised to speak.
You mean... Like... A private message system?
The purpose - the only purpose - of creating a Gallery room is to be able to chat without getting interrupted by folks who aren't invited. Allowing them to interrupt anyway subverts this purpose. There's a button that lets you request access - if you do so, and your request is denied (or later revoked), that is the end of your dialogue with the room owner(s).
I'm always delighted by how many proposals for some form of private messaging involve an explicit desire to contact people who've already shown that they don't want to be contacted. It's a welcome reminder of why we don't have any generally-available PM feature.