Not disagreeing, though in terms of the Kickr, or at least the model I have, the only measurement that is made is the (angular) velocity of the flywheel.
My understanding, albeit I haven’t really read into this too much, is that the Kickr knows the mass of the flywheel, thus inertia required to accelerate it and ultimately how much power has been applied when there is a change in flywheel speed.
My BIG assumption in all of this had been that due to a square law in rotational inertia a doubling in power at low flywheel speed makes a noticeable difference to flywheel speed thus was easier to respond to. Conversely, at higher velocities, doubling in power might not accelerate the flywheel all that much.