A command called "Duplicate Pattern as New Variation" could be cool but honestly you should just explore the variation system.
There's a whole Variation system which allows you to create and re-use patterns. That's why it doesn't work the same as it does for Audio and Instrument Parts. If you click the "i" (for info) icon in the top left of the pattern editor you will see a whole menu that makes it pretty clear.
There are some keyboard shortcuts for this too, Duplicate Variation, New Variation, and Delete Variation.
So what you do is press "D" to duplicate the pattern, then either press on the Duplicate button in the Variation menu (opened by pressing the info icon in the pattern editor) or you press a keyboard shortcut for Duplicate variation, which I have set to CTRL + D on Mac.