I suspect that sevenlayermuddle and I are at cross purposes. I'm talking only about a certain class of system where the processor has a certain fixed job of work to be done, and it gets it done in a fixed n clock cycles, which takes some unknown but variable amount of real time time as we can change the clock rate. When the cpu has done its work the clock gets turned off, goes to dc. This is how those old machines that I worked on worked, power was higher if clock speeds were higher but cpu_power * time = cpu_energy was a constant in the case where there was a fixed job of work. The model was that you move a certain amount of charge from one charge cell to another at each transition.
(As for inductance, thinking back across forty years, higher slew rate means greater back emf and greater change-opposing currents through resistive wires but slew rate isn't so easily associated with clock speed as after all these are approx square waves were talking about, very far from sine waves. Higher slew rate then means greater joule heating power but for a shorter time as the voltage swing is constant. But again we don't just automatically get slew rate from clock speeds, so we have no help; a slew rate could be very high even for a low clock speed for all I know. My ignorance of electronics is almost boundless.)
That is not to say that real modern machines or real workloads work like this, and there are of course the constant current draws such as the screen, NIC, other i/o that has to remain awake and so on, but the latter work in favour of my argument of getting things done faster so you can switch everything off sooner, but it's only relevant if you actually do that.
Anyway, I defer to sevenlayermuddle who cannot possibly be as fuzzy and foggy as me.