In recent versions you might have to hover for the icon to appear, which is infuriating.

Except for that, all proxy icons should be dragable without problem if they are from the native widgets (so no guarantee for misguided developers who reimplemented it to look like the native one without actually implementing its behaviour). There might be a small delay between the moment you click on it and the moment you can drag it, to avoid mistakes (I think that was the case at some point, not really sure now).