Ability to make New Windows fullscreen (for secondary monitors)

I love working with blender in full screen mode, no distractions!

But: when I have a Cintiq plugged in for drawing, and tear off a panel to view on the second monitor (shift+click in the corner to tear off a panel, or use New Window) there's no option to have that full screen as well. Not a disaster , but just kind of annoying. I don't want to be wasting my precious pixels on an ugly Windows title bar. Let me cover all my monitors with nothing but Blender please :-)

There is a sort of workaround (use New Main Window instead of New Window) but then you have two sets of file menus, one on each screen, so it actually doesn't save you any space.

This is a tiny feature but I think it would make a lot of perfectionists very happy, and I hope it's not too complicated to implement :-)