I don't mean to sound rude, but did you even read the answers to the link you posted?
One of them shows this blueprint which wouldn't use the global menu for the desktop version.
https://blueprints.launchpad.net/ubuntu/+spec/packageselection-desktop-n-specialized-unity-form-factor
So it seems the desktop version would have room to innovate when it comes to the menu. Do you have any particular ideas?