I don't think you're getting the main point. The only application that this physical device would run is ChatGPT (or some successor). You won't be able to install other apps on it like a normal OS. Everything you do is inside this LLM.
Underneath, it can be Linux, BSD, Unix, or nothing at all, whatever. It doesn't matter. That's not important.
OS was just a convenient phrase to describe this idea.
I got your main point from the first message, but still don't like redefining terminology like OS to mean what you did.
Think of iOS and everything that it does such as downloading apps, opening apps, etc. Replace all of that with ChatGPT.
No need to get to the technicals such as whether it's UNIX or Linux talking to the hardware.
Just from a pure user experience standpoint, OpenAI would become iOS.
I don't think "OS" means anything definitive. It's not 1960. Nowadays, it's a thousand separate things stuck together.
I think what you mean is "Desktop" not "OS". You're just replacing all the windows, menus and buttons with a chat interface.