What you're saying is equivalent to insisting that measuring the length of a line is impossible because there exist optical illusions that trick us into misjudging it.
I think you just proved my point. Yes, you can measure the physical length of a line with a ruler and I was never saying you couldn't, but knowing how a
human observer will perceive the length of the line requires a psychological model of their length perception. Illusions aren't "tricks" - they are demonstrations of the inferential assumptions our perceptual and cognitive systems make to understand the physical world. So when we see an illusion such as this the
Müller-Lyer Illusion the point is 1) your visual system makes assumptions other than the retinal distance subtended by the inputs; 2) one needs a
psychological model to understand and predict the way we actually perceive line length. If you are only interested in measuring the signals coming out of audio reproduction equipment, you don't need to worry about people, brains, etc. You can just measure lines. But someone asked about how measurements relate to the sounds we experience. In that case, one needs a PSYCHOLOGICAL MODEL (I am shouting now) to understand the relationship between the physical stimulus and our experiences. And these models are often complex, non-linear, and, sometimes, not well understood as yet.
No one is saying it is impossible to measure the physical signals. But that doesn't tell you how they will be perceived. Which is what matters if you actually want to
listen to those signals and hear music.