It is often asserted that one can't make meaningful comparisons without putting the microphones in the same place. I have always wondered why. If room correction system requires extraordinarily precise microphone placement to confirm its effect, I think the best word to describe that system is "unstable."
In fact, my experience measuring the effect of room correction systems suggests precise microphone positioning is unimportant. Let me give you two examples, the measurements of Audyssey XT32 in my reviews of the Marantz AV7702 SSP and Denon AV-X4100 AVR.
https://hometheaterhifi.com/reviews...rantz-av7702-surround-sound-processor-review/
https://hometheaterhifi.com/reviews...eceivers/denon-avr-x4100-a-v-receiver-review/
Sorry, SECRETS does not have links for sub-sections. You have to scroll down.
To summarize, in both cases calibrated Audyssey conformed the sound power to Audyssey's target curve. Perhaps there would have been more error with less well behaved speakers. I do not know, and have no interest in testing that case.
In both cases, I took the Audyssey calibration measurements at the positions indicated on the TV. D+M's GUI does a good job of walking you through the Audyssey calibration process. My confirmatory measurements were taken in a 6-point bubble around the primary seat (Geddes and Blind sound power method). I did not document the specific microphone locations during the AV7702 review, so I could not have copied them for the AV-X4100 review even if I had wanted to. Yet compare the results! The variances are well within measurement error. That is even more remarkable when you consider that the calibration microphones were different, and the Audyssey tower microphones are not individually calibrated.
Also, I believe that ARC came out statistically no different from no EQ in the Olive study with B&W speakers. The systems that beat no EQ were, from memory, the two different Harman systems and whichever of RoomPerfect or Trinnov was tested. Audyssey was worse than no EQ. I think Anthem's subsequent updates to their target curve fixed the bass problems Olive measured. Note also that Olive tested a wide bandwidth speaker, not a bass managed system.
Lastly, while I agree in principle with you that "at least some of that advantage [from integrated BM and EQ] can be obtained by manually tweaking BM, EQ, etc. with independent measurements," who wants to do that if you don't have to? Practically speaking, even most techie-inclined listeners will just run the calibration and judge resulting the sound quality. At most, one will play with the target curves in Dirac, ARC, or the Audyssey app. I think the bottom line is that room correction and bass management both substantially apply to the same speakers operating over the same passband. Therefore, they should not be considered in isolation from one another.