The overlay title and tabs should be inside the child window, not the parent window

The overlay module does some complex things with the title and local tasks (tabs). These are prepared by the child window (inside the iframe), then grabbed by the parent window's JavaScript and placed inside the parent window, outside the iframe. This leads to a lot of awkward code and getting rid of it would quickly solve a lot of bugs, among them:

#725734: Overlay doesn't escape any page titles (residual cleanup)
#782652: Shortcut-specific code shouldn't be in the Overlay module
#682884: jQuery ui sneaks in an undesired font-stack for overlay headers and tabs (see also #700832: Parts of the overlay inherit CSS from the underlying site theme, leading to a font mismatch in the overlay page title)

So is there any reason it really has to be done this way? I guess it's to achieve the transparency - but is there no way to make parts of an iframe transparent so that the underlying parent window can be seen underneath it? (If that is in fact the reason, then I think #782096: Radically alter the look of overlay header would help with that.)