My power meter had a red 3 1/2 digital display with .1 watt to 199.9 watt and a switch for 1 to 1999 watt. It was directly connected to the mains through a current transformer , no hall effects. With .1 watt sensitivity I could tell if a VRC carriage was sticking when going up or down or if the tape guild pins had too much friction when going to play mode. Your idea of monitoring current on a scope opens up new possibilities. I could see how the ESR of the main filters condenser could be guessed at by monitoring the inrush current from a cold start.

Interesting side note. Most smart phones have a 3D hall sensor to sense the orientation of the phone relative to north south poles. If you move a magnet over the back of the phone you can find the sweet spot where the 3D hall IC is located. Put an X on that spot and you have a DC current meter for free. Not the best current sensor but in a pinch it gets the job done.