In RF context, voltage is not a size that exists. It simply does not appear in any place that describes a wave, directly.
What is "voltage," for an electromagnetic wave, eecs, before we can talk about how to measure it? You need to first convert your wave into something you can observe directly, which involves termination with a specific impedance, which makes the measurement frequency- and waveguide-specific.
Also, as Kevin said, proper observation will change the impedance of your system, so that a good measurement cannot be done in-system l, because it affects the system so significantly. (But this also applies to power measurements).
Power on the other hand is always easily definable: how much hotter does this 1g of material get if it absorbs all the power for 1s? Can directly derive the power sunk from that.
Even when we are ok with having to unplug the system, and know the characteristic impedance of the port we attach to well enough (we usually can't know) so that we can match our measurement equipment to it, there are still technological challenges that make observing power easier than observing voltage or current:
- Power is always positive. So if I have an analog circuit that converts power to a current (and quite possible also incorporates correction factors for different frequencies, because the real world is never an all-pass), then I can just integrate that power with a capacitor. Read the voltage over the capacitor every so and so many seconds and to get an estimate is how much energy passed by in that time. Energy per time is power.
if you were to just build a circuit that takes the integral (or average) of current or voltage as found through converting some wave to that using a specific impedance feed, that integral would mostly be 0, because we already know the signal is zero-mean, no matter how high the amplitude are.
- A pure electromagnetic wave without modulation has constant power over time. The current or voltage you could measure changes as often as its frequency dictates.
For modulated carriers, the power changes at the speed at which the modulating signal changes power, not at the frequency of the carrier wave.