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Yes.

Creates a short-lived channel per chat. It works well in terms of sharing responsibilities with a team and allowing people to jump in easily.

I did feel a bit of unease with having customers in the same place as our "private" conversations.

Shameless plug: My project, Cactus Comments[1] does something similar, although for commenting, instead of support chat.

We ship a web-embeddable Matrix client. The users' browser connects directly with a Matrix server of their choice (or a default one).

[1]: https://cactus.chat

This is very close to what I had found a need for today - now if only I had a (self-hosted)-wordpress-user-accounts bridge for the login -

and auto-prune to delete all messages after X number of hours - a new project could happen quickly with this.

Yup! To be honest, a lot of the smaller teams using Papercups with our Slack integration rarely need to interact with the admin dashboard if they don't want to. (But it turns out that having a dashboard to manage unresolved questions, add private notes/labels/tags to customers/conversations, etc. is still pretty helpful)