Yes, the smoothness of the off-axis is what we know matters for preference, but it's not the only thing. Smooth directivity, which I of course think is always good to have, is generally used in the sense of the reflected sounds being similar to the direct sound. I'm just saying in addition to the 'shape' of the off-axis sound, overall SPL matters too.
Anyway, most of my 'education comes from Toole's book, but I've read most of the papers being cited. I think it's not secret that Toole is generally in favor of wider directivty/louder sidewall reflections.
Going to the research though, here's Toole in his book (7.4.2) talking about Toole (1985), a double-blind test that was specifically about directivity:
"In these tests a loudspeaker with narrower dispersion, but with more uniform output off-axis, was given lower ratings than two loudspeakers with wider dispersion, but uneven output off-axis, suggesting that some amount of laterally reflected energy is desirable, even if it is spectrally distorted."
It's an old study with old speakers -- the Quad speaker here was definitely narrower than most of what we might consider 'narrower' directivity on this forum -- but still one of the best we have on this specific matter.
Relevant to
@richard12511's question about how much width is optimal, a pair of studies by Klippel in 1990 found that feelings of 'naturalness' and 'pleasantness' were 50% and 70% related to spatial qualities, respectively. This study is in german so I haven't read it myself but Toole says about it(7.4.5):
"Klippel chose as his objective measure of “feeling of space” (R) the difference between the sound levels of the multidirectional reflected sounds and the direct sound at the listening location....
[snip]
...The optimum difference between the direct and reflected sound fields is about 3 dB for speech, 4 dB for a mixed program and 5 dB for music. There is no frequency dependence considered in these numbers, and we know that most loudspeakers do not exhibit constant directional behavior at all frequencies.
A good loudspeaker for this purpose would therefore be one that has two qualities: wide dispersion, thereby promoting some amount of reflected sound, and a relatively constant directivity index, so that the direct sound and reflected sounds have similar spectra."
Here's the accompanying graph:
View attachment 132088
So although these studies didn't test for the spectral quality of the reflections (the 'prettiness' of the off-axis), they do imply that all else being equal SPL alone is enough to be a contributing factor to the perceived naturalness and pleasantness of a speaker.
Toole 2006 is a great paper, a review a bazillion different studies on reflections that talks about many of the most interesting revelations in Toole's book in a slightly more analytical way. One takeaway from this study is that early reflections in a typical room happen around the zone where 'image spreading' is found, which is generally perceived as a positive effect.
Some assessment of the effects of directivity can further be inferred by studies on sidewall reflections vs absoprtion/diffusion, since it's essentially much the same thing to the listener. There have been a few studies showing reflected sounds are preferred to absorption for mastering and recreational listening.
We also know from Shirley et al 2007 stereo listening degrades speech intelligibility (although admittedly this is not the same as clarity) due to interaural crosstalk cancellation and wide directivity/louder sidewall reflections help combat this. And then I believe Toole said he thought the Salon2 beat the M2 because of the wider directivity.
It's also worth noting that the Olive preference study did not look at horizontal directivity width, it just looked at the overall DI curves, which are unreliable at describing horizontal directivity.
One could also consider the existence of the revels themselves, which consistently demonstrate wider directivity than most other speakers with prominent waveguides, with the Salon2 being particularly wide up to about 10kHz
These are just the things I could think of off the top of my head. So I don't think it's not entirely unreasonable to believe that wider directivity might be slightly more preferred for the general populace especially considering Toole seems to think along these lines too. No doubt wide
and even is better.
