Bike fit / correct riding position

I like the idea of using someones shoes size to figure out their frame size.

It is not as absurd as you might think. To the extent that one can correlate bicycle fit with limb segment measures it works out relatively well. Footlength is not just strongly linked to height--- shorter people have smaller shoes--- but comparatively longer feet generally indicate comparatively longer leg bones. Foot length also typically matches the length of one's forearm. Since the elbow is typically at ones waist it is a pretty good guide to both reach and setback. Height is quite well linked to tibia length. Take two people of the same height. The person with the longer feet will probably have both longer legs (shorter torso) but also longer forearms and longer femur, whence more setback..