Also it does not work if the floor is even and one leg of the table is shorter than the others, which I suspect is the reason for the "wobble" in many cases.
IMO this proof is a good example of science taking itself much too important.
Is it? My experience is that most of the time in practice uneven legs of four legged objects are within a small enough tolerance margin that they can be considered mostly equal, but floors are surprisingly less even than we initially suspect, their vertical variability being perceptually dwarfed by their overall surface.
IMO this proof is a good example of science taking itself much too important.