I've always thought that on-car balancing was a way to cancel the balancing tolerances. Even if the rotating parts of the axle and disc are finely balanced and the wheel and tire are also, they are still not perfect. Unless you are willing to remove and replace the wheel assembly, moving one pin (or lug stud) at a time, on-car balancing is the only method to offset the errors. Having said this, I don't know if modern on-car balancing equipment has the ability to do this with the required precision thereby gaining you anything.
BTW, this thread apparantly uses the terms rounding, truing and shaving interchangeably. I think shaving is used to reduce thread depth and thus flex and improve cornering. Truing/rounding takes off only the high spot(s) and hopefully leaves maximum thread for the buck. Either method improves on what comes out of the mold but since rubber has plastic and elastic properties, it will never get TIR's with great precision or even repeatability. I once read that F1 tires are hydro-pressurized and then trued. I dunno for sure.
As for ply overlap, it would seem that would cause a bump sensation, not indicate an out of round or balance problem. Unless running on glass, it would be hard to pick out.
Naw, you can't balance a square tire.
Good point.