Supervisor mode is basically operating system configuration stuff (DNS, audio, etc.) telemetry for the dev team, and health checking: https://www.home-assistant.io/blog/2020/09/16/supervisor-joi.... (Unless I'm missing something?)

It seems fine that this isn't available in docker, since you can do all of this via docker and your host's configuration system. It would be nice to have a GUI for it, but if you need a GUI then you probably aren't running HA via docker, you used their image.