Ok but why compensate for it? Wouldn’t the mixer have mixed to what he hears?
There's nothing really to compensate for at the mixer for cross-talk, other than the 60's approach of simply panning things hard left and right. I was watching some of the videos from the last Munich audio show to see what was there and one thing that seemed to pop up was older classical recordings, and it was perplexing as to why they were using them until I listened to them directly. The older recordings have things panned to much greater extremes than modern classical recordings which try to approximate (or just simply record) the actual orchestra as it is. In a sound demo, this will give an artificial sense of having a more spacious sound stage than you would really get. I guess they feel that the subjective value exceeds what the older recording loses in terms of fidelity, even though some are still quite good by today's standards.
For XTC, the corrections are applied within the system, and not from mixing. Mixing can help, but that is to enhance the subjective perception of the recording, and not deal with XTC per se. If you were to mix on an XTC equipped system, I would think there is a good chance you'd end up with recordings that sound myopic closed-in on conventional stereo setups. Basically the opposite effect when going back down to regular stereo. On my setup, I do have to compensate for the head shadowing and the reduced SPL that results from about 1 kHz on up. It gives a strange looking measurement with an elevated treble response that's inversely proportional to my specific HRTFs, but is perceptually neutral. However, if I listen through the measurement mic using IEMs to music, the response in the bass and lower midrange is correct, but it gets screechy bright above that due to the fact that the mic records both speakers simultaneously. While there have been various attempts, I don't think its something you would want to do as it would be a mixed bag for many listeners. Some it would help, others not. An example of "not" would be typical pop recordings that are mixed to sound good on things like inexpensive headphones, car stereos, and in-ceiling systems at restaurants.
As far as the stereo recording format itself being "flawed", I don't think it is fundamentally. Done correctly, its the most accurate method, better than multi-channel setups I have heard. But the huge caveat is that its the most difficult to get right since you only have two speakers, and both you and the room have to be integrated into the response to get the correct transfer characteristics, or it doesn't work. In that regard, multi-channel setups make more sense for general use since there is more flexibility with having multiple channels. On the flip-side, proper two-channel setups actually allow the sound sources in the recording to be perceived as the origin of the sound, and not the speakers themselves. This gives a unique experience in that the contrast is jet black, and the sound immersive, vivid, and natural. There's no real sense that you are actually listening to speakers. This is something I don't get out of headphones. Maybe there are some headphones that do get there, but I have not had a chance (nor probably ever will) to sample things like the HE-1. But with speakers there are so many variables, and so many obstacles to overcome, which is why I think it's on a trend towards being relegated to relative obscurity in favor of multi-channel speaker setups and binaural methods for headphones and IEMs like what Apple has.
But, all of this is quite far from the original topic on the face of it, but in some ways its not since the reflections are both a desirable and undesirable characteristic at the same time, depending on how much and when you have them in relation to the direct sound.