I only have one third-party icon in my menu bar (Dropbox) and it can’t be dragged out of the menu bar. I don’t know whether that’s the case for all third-party

I only have one third-party icon in my menu bar (Dropbox) and it can’t be dragged out of the menu bar. I don’t know whether that’s the case for all third-party icons. It is. Apple has their own private API for their "menu extras" and actually loads them into the windowserver itself. It's a major PITA to support one of these things, so only a very small number of third party apps choose to do it. The alternative public API is basically just a tiny window for each item sitting in the menubar. There's no technical reason why Apple couldn't implement the same kind of command-drag behaviour, but thus far they haven't.