I modded many guitar amps over the decades. Many had pre-PI masters, which didn't have enough gain stages before the master to develop decent distortion...like silverface Fenders. Changing the pre PI master to a post PI master (I usually used a stacked dual pot, but sometimes used a cross-line master) improved the quality of the distortion greatly.As will the rest of the tube stages. How do you differentiate?
In the early 80's, the Sholtz Power soak and to a lesser extent, the Altair power soak were popular especially with non-master Marshall players in our area. I put quite a few post PI masters in non-master and pre PI master Marshalls belonging to players who were using power soaks, and got to compare the tones of all three...pre and post masters, and power soaks.
The PI is part of the power amp. The tube stages preceding are part of the pre amp. True that all overdriven stages add to the distortion picture in an amp, as well as transformers, power supplies, speakers, etc. My original point was that players usually refer to "power tube" distortion as being "superior" to preamp distortion, but do not realize the breakup of the PI, then amplified by the power tubes, IS the sound they are hearing.