I don't know of any research that's studied this directly, but Harman's research into room curves dealt with it indirectly, in that it found that with flat on-axis measuring speakers listeners preferred a downward sloping in-room response. This must be partly the result of most flat-measuring speakers having wider radiation in the lower frequencies. It's not clear though AFAIK whether this is the room curve that listeners would have preferred had the speakers used been constant directivity right down to the bass (e.g. like Dutch&Dutch 8C, Danley Synergy series, etc.). AFAIK the Harman research used only speakers that had a downward sloping power response. I'm really hoping that Harman or someone else with the resources to do it properly does further research into this using a greater variety of different speakers, including true constant directivity designs and even perhaps omni, dipole or bipole.
Other relevant (also Harman) research into room correction DSP basically found that, below the Schroeder frequency, a smooth in-room response is more important than a smooth on-axis response, while the opposite is true above the Schroeder frequency. This would imply that baffle step compensation is necessary down to the Schroeder, but not below it (there are lots of opinions on this though and I don't think it's a settled question).
The way I see it, a lot of designers of home audio passive speaker have in fact basically been working on this principle for many years, by basing decisions about baffle step compensation on the size of the room the speaker is likely to be used in.
I think it's doubtful that trying to sacrifice the on-axis response to accommodate the room above the Schroeder frequency is a good idea (of course, the Schroeder frequency is a pretty slippery concept IRL and it's exact frequency in a given room can't be exactly defined).
My personal view is that room correction below the Schroeder frequency is important in small rooms, and that you may as well start with a speaker that measures flat on-axis and then correct from there. But where this is not possible or desired, the next best scenario would be a speaker that measured flat on-axis down to the Schroeder frequency and then - in very small rooms at least - gently slopes down a bit below there.
This makes passive closed box speakers a little more attractive in small rooms perhaps, or ported speakers that are tuned a little lower than textbook, giving a gentler, slower roll-off. It's also one reason why active monitors might not sound as good in small rooms without room correction: they tend to be (hopefully) ruler flat down to the their lowest frequency and then roll off at perhaps 48dB/octave below there.
Great explanation!
The question is, I think, whether the brain automatically compensates for any spectral imbalance caused by the room, baffle size, etc. I would tend to think it does. With regards to Harman’s research, there’s too many unknown variables, I think: how do we know that the preferred «flat» speakers were not simply better speakers overall? Do we know it was due to baffle step compensation?
Here’s a simple way to investigate this: use high-quality flat headphones as a reference (adapted to the ear canal etc of the testee). Compare it to two identical speakers, one with and one without baffle step compensation. Which speaker sounds most identical to the headphone reference? Et voila!
But unfortunately, the field of applied loudspeaker research is small, so unlikely to be undertaken professionally...