I'm not questioning whether it makes a difference, everyone would seem to agree that it does. I'm interested in finding out WHY it makes a difference.

The reason posited by most is the increased inertia that a flywheel provides improves stability, but the math doesn't support that assertion. For a solid disk of even density, the formula for rotational inertia is Ir=(m*r^2)/2 where m is mass and r is the radius (note that there is no speed component in the formula). So for a 20 lb, 12" platter the result is 360 and for a 12lb 3" flywheel it is 13.5 or ~27x smaller. Now, adding a periphery ring to the platter would definitely help more as the mass is concentrated at the largest diameter (although the mass is smaller compared to the platter). I just don't see where a smaller, lighter flywheel has that much of an impact at least on inertia, angular momentum or kinetic energy.

FYI, a properly designed speed controller will provide excellent instantaneous speed stability, but long term speed accuracy is improved with feedback.