If you shoot 10 rounds, and measure and average the PSI, you'll get an estimate of what you'll get on future samples out of the same lot. When you shoot that second sample, the number you get will almost surely be different from the first. And the next sample will be different still.
So PSI does not perfectly predict PSI. And CUP does not perfectly predict CUP. Using my formula to predict PSI from CUP is no different. You get an estimate that is about as good as random measurement error and cartridge to cartridge variation allow. The formula works between about 30,000 PSI and 65,000 PSI. Below that, curvature takes its toll.
CUP, of course, is fading away. In time, it will become a historical footnote. Modern strain and piezoelectric methods are better.
As stated, the old CUP method was formerly taken as producing a true PSI number. If you read Ackley, he published what he thought were PSI numbers, taken with a copper crusher. That's why some his numbers seem so strange today. They are really CUP numbers. The CUP system does produce decent PSI numbers at lower pressures. At higher pressures it does not.
So, the formula is useful if you're trying to understand Ackley and other writers of that era, and it's useful if you're working up loads for a cartridge that has only a CUP specification. I ran into that when I instrumented my milsurp 6.5x55. I needed the equivalent PSI number, and couldn't find it.
A chronograph is your friend. In skilled hands, it is the most precise indicator of pressure that most folks have. Some loads in some cartridges will increase MV with increasing load in an orderly fashion. Others will begin to plateau. If your load plateaus, you should not continue to increase your load. I've run into this a couple of times. In one case, switching to a magnum primer fixed the problem.
So, why is it that we don't we all simply go with PSI?
That is the way that the world is heading. Before about the 1960s, equipment was not readily available to do PSI. We used CUP because that's pretty much all we had.