If the apps could use the real pixels instead of a "retina 2x" mode, there wouldnt be any problems. Those things are apple-specific implementation details (badly designed imho).
Apps can use 'the real pixels'. The lastest builds of Final Cut Pro X and iMovie can show full 1080p video at native resolution in their tiny 3-inch preview windows, and most games will let you set the resolution to the native 2880x1800 .
That wouldn't actually improve this situation, though. Showing this image at native resolution would make the text not be pixellated, sure, but it would also be near-unreadable at 1/4th the size.