Some thoughts:
In order to design a speaker without listening, we need targets of course. So here are some, perhaps incoherent, thoughts.
In terms of amplitude response the original studies dictate a flat direct sound, and smooth off-axis performance.
For those looking more closely, the actual preferred slopes (regression) can also be deduced. So we have a very good idea of how a loudspeaker needs to behave in terms of frequency response.
A couple of potential discussion points:
-The original tests were performed mainly using standard forward firing cone/dome loudspeakers. A couple of loudspeakers using a horn were also present, and one dipole. We know the latter had a severely compromised frequency response.
-From blind tests we know while the better measuring horn loudspeakers could still win blind tests compared to loudspeakers with flawed frequency response/directivity issues, they tend to lose compared to equally good forward firing cone/dome loudspeakers as far as I have seen (there was the blind Salon2 vs M2 test on AVSforum some years back).
-Recently we've seen different designs, such as cardioid patterned speakers, become more prominently available. I've been looking at more studies involving half-space designs (in-wall) as there is correlation there, although also not entirely of course. Less energy vs no energy towards the back (cardioid vs in-wall).
Although I cannot find with absolute certainty what is the deciding factor in preference when it comes to off-axis sound. Is it the smoothness of the curve, or is it the regression slope?
Using Gemini: "The Preference Intervention: In actual practice, the "target" for in-wall speakers is simply linearity. The research (Welti/Olive) suggests that for in-walls, listeners prefer the smoothness of the slope over the steepness of the slope."
But is this the case? I haven't been able to track any specific studies with more technical information and certain -quite credible- reports, have noted that non-standard cone/dome loudspeakers have a tendency to not sound entirely balanced at times due to the nature of the slopes, while smooth, being shallower - which is then countered by manual intervention (tilting).
And then there are constant directivity loudspeakers, which present a unique challenge because their ideal anechoic performance contradicts the ideal statistical target for a standard room..
/rant