Wow. Lots of theoretical mathematics! I agree with you. That is one of the reasons why there are so many different types of speakers and amplifiers, etc. out there. Not everyone hears the same. It is highly subjective. If one looks at the output of a tube amplifier versus solid state, some people prefer the sound of the tube which typically has a lot more distortion. It is the type of distortion that is "pleasing" to some ears. I think that some people can hear the phase distortion, albeit subtley. They may use the term "more transparent" to describe an amp with a large frequency bandwidth. I know there are lots of people who don't hear the difference.
I guess what it comes down to is that a lot of manufacturers use the numbers game to play into marketing. For some people, the numbers seem to be a significant factor. Others don't care and are happy with a HTIB. Then there are those who can hear the difference. Those are the most unfortunate as they end up shelling out big bucks for what they perceive sounds better.
I would always caution someone who asks "what is the best ...?" with respect to home audio equipment. While someone can be given a myriad of options that may sound great, it comes down to what sounds good to their ears. Perhaps the best advice comes down to what their budget can afford? That is where I find Axioms great due to the "bang for the buck".
