You are missing the point, that doing it digitally do not have the inherent difficulties that the analog filter designers have to face. Try solving an analog design issue or optimization that requires Laplace and Fourier transforms!! Using computer programs, you don't have to be an EE or mathematician to do it well. You obviously have electrical/electronics knowledge so you should know that full well, so sorry about stating the obvious.
Of course, and they seemed proud doing it in the time domain. Audyssey, and I am sure Dirac, Trinnov and others all play in the time domain, one can assume some do it better than others, but the top sellers all do, except I am not sure YPAO, only because they refer it as PEQ so I do not know that for sure.
Let's be fair, you know what you do, but I doubt you know what Audyssey, Dirac Live, Anthem ARC do, and they all seem to be very protective (rightfully..) of their proprietary stuff. No offence, I do have faith in the NA Ph.D programs, as I do in the medical programs

, at least those who subsequently worked in their field of expertise in both related industries and reputable universities.
You should know by now that if it is something I "think", or opine, I usually would say so, otherwise it is not what I "think", and I have not said anything about DPLIIx.
I assume you are just stating your opinion based on your own experience that may or may not be mostly subjective. Incidentally I like DPLIIx too, but I am not sure if I'v lost sleep over losing it to DSU, even though I don't have any height speakers yet.
Audyssey never stated they even touched the phase in the higher frequencies, and you can limit its effects to the subwoofer only, or with the App you can set the upper limit too. Also, I have plots to show their effects on phase shift for the lower range, no evidence of your claim, that you are so "certain" about.
Totally subjective, and highly dependent on how you set things up.
I am a lover of classical music. I also know Audyssey is far from being a perfect solution. I fully agree it cannot(no REQ can, I would think..)make bad speakers sound good, or make less accurate speakers more accurate in most rooms.
Again, I do not think Audyssey (and others) is perfect,
far from it. For one thing, I know in my room(s),after each Audyssey run, I have to manually set the crossovers to order to get the best looking FR graphs. For example, the difference between XO60 and XO80 for my FR and FL are very significant if plotted with FR+FL and subs on, or all 7 channels+subs on, yet with the FR+FL or subs only they all look good. As I mention, I really like your idea of variable/user adjustable crossover slope as I "think" that is at least one reason why Audysessy could not do better in integrating highly bass capable speakers with the subwoofers. Audyssey claimed XT32 has the resolution to integrate, even for the "large" setting, but I know it is not the case for my setup in my room. I do give them the benefits of doubt, that they don't have control of the "slopes", but this is just my opinion, and I do believe it could also be
one of the reasons why there are no consistent views on the effects of REQ in their rooms. It may also be true that not everyone would prefer more accurate bass response. Dr. Toole obviosuly thought most people do prefer more accurate response but I suspect he would also agree that may not be the case if we focus on the lower range say 20 to 120 Hz for example.
It seems to me you are really just stating your subjective view (not necessarily facts), and one that seems somewhat extreme. I wouldn't "advice" anyone, but would suggest that people be open minded, research the topic while paying less attention to subjective views, and then try what they have and paid for. If Audyssey, YPAO, or whatever, offer no improvements, then try the bypass option, or turn it off completely.