Why do Whirlpool and GE vertical modular washers have an inductor in series with the capacitor? Doesn't that undo things? What would happen if the inductor was bypassed?

If you knew you would have answered my question.

My theory is so the inductance shifts the leading phase angle just enough so you can get more current through the motor's aux winding without causing an excessive displacement between the two pulsating fields as happens when a capacitor exceeds a certain size.

But its just that a theory, I honestly have no way of knowing what the engineers were thinking.

Yup. When its not in the capacitor itself its a coil of wire underneath the tub. I remember the portable VMWs did not have it.