If you want to time travel a bit, OpenWindows / OpenLook was very clean.
How clean? Literally nothing on the desktop.
Everything was accessed through an easily (re)configurable context menu.
By default there would have been absolute necessities on there but precious little else. It was up to the user to edit the config to add programs to it. Kind of like a forerunner of the Quick Launch toolbar or the Dock.
That said, I seem to recall it was possible to put launcher icons on the desktop too, although that is also where programs minimised to in icon form (Windows 3 used to do that too), so maybe I'm wrong about that.