Fred should be ashamed of himself for abusing anybody prepared to experiment and learn!
I think there are several common assumptions that you could prove wrong with this experiment (I've done it myself).
Clearly the flats win in terms of reducing vignetting. Absolute must have with just about any imaging system (you might get away without it for awhile with some tele lenses but not when you start pushing it).
Unless you had a camera with serious amp glow or other large scale artefact, dark subtraction will not show at all at the resolution of the images you've presented.
Can you give us a 100% crop from one part of the image with and without darks. I believe that there will be less difference than most people expect. The darks can only reduce hot pixels (things that are constant from one image to next). They can't reduce the random noise which is all that will be affecting 99.9% of the pixels in the image (from a high quality CMOS sensor).
Depending on what software you are using (eg ImagesPlus), you can tell it to use the dark frames to only subtract the hot pixels from the light frames, which prevents it adding further noise to other parts of the image (by subtracting one lot of random noise from another). It also means that a slight temperature mismatch between lights and darks becomes less of an issue.
I applaud all experiments!
Phil