Yes, Docker is effectively acting as the supervisor process for this container, only managing its process lifecycle and allowing easy removal/persistence.
My (linux) desktop has a macOS icon on it. I click on it. That starts a QEMU/KVM process which runs macOS. When I quit out of that, it is gone. When I click on it again, it runs again.
I suppose there are a few files floating around that persist between runs, and are not utterly trivial to manage. Just ... trivial to manage.