I keep trying to explain this, BACKGROUND RESOLUTION is NOT MONITOR RESOLUTION. When you set it to 2048x2048 your monitor will not suddenly display at this resolution. So stop comparing it to your monitor resolution. As explained, it is simply the resolution at which the game RENDERS 3d polygons in MEMORY before it display the image.
How does this improve image quality? Simple. Open any image editor with two images taken on any decent digital camera. One at 640x480 and another at say, 1600x1200. Now, blow up the 640x480 image to 1280x1024 and shrink the 1600 one down to that res. Which image looks better? The one that was large and reduced.
You lose serious quality going from small renders to big ones just like small images to large.
And if you still doubt this process after all those screenshots I got nothing to say other than to try yourself. (You don't have to edit the registry, just use the config tool and check the difference between 256x256 and 1024x1024, it IS noticeable).