Not a perfect choice of terms I freely admit. In my own experience, I last used non-virtual, mutable, long-lived servers over 8 years ago. Since then it's been a progression further away from that style: PaaS, immutable infrastructure, Heroku, and currently a mix of AWS Lambda and Docker.
You can deploy it exactly the same way as anything else, it's just a matter of being willing to sacrifice some of the features if necessary. You don't necessarily even need each of the features on each project so it's entirely reasonable to deploy exactly like you would anything else.
There's a Redis adapter for Phoenix channels that you can use in environments like Heroku where clustering might not be an option.
If you want to use built in Mnesia database on an immutable or cluster, attach block storage and configure it to store to that disk so you can remount when you deploy your immutable image.
Hot reloading is the only one where you NEED mutable servers.
(I don't agree that your other assertions are correct, but I'm most interested in this one.)