I don't know if much innovation is really required, honestly. You probably won't find what you're looking for with Mac/Windows, but if you run a tiling window manager like i3 on Linux you'll pretty much just see a clock, some system stats, and whatever applications you have open on the screen. You can pretty easily configure the bottom bar to remove the superfluous system stats, or even the clock if you want.

Is that the kind of experience you'd look for in a distraction-free OS? If not I'd be interested to hear your ideas - I use i3 for work but manage to distract myself anyway because I always have a web browser open.