> The only problem is that the anmount of electrons you have to push through the transistors has a quadratic dependence on frequency.

I don't see how this is ultimately true.

The amount of electrons needed to flip a capacitor is constant given that the voltage is constant. The more often you flip, the more current you need per time.

The amount of electrons needed to flip a capacitor is proportional to the voltage. So, lower voltage means a) less power per electron and b) less electrons. Therefore the power is quadratic with the operating voltage.

Third, if you want to increase the frequency, at some point, you have to increase the voltage or you get errors. Then you increase frequency and voltage at the same time and your power consumption shoots up.