This concept of a speaker playing nice with the room comes from the 50s. Bose was the early pioneer who exploited the concept mostly with a lot of marketecture. While everyone, including me, laughs at the Boses, there were a lot of things he did right. I can drop my 601 series III in any room, and to the untrained ear, they sound great! In fact, if you have an open concept, and are listening to music while grazing around, they are terrific! One of the things he did right was to kill the bass. In any typical room, bass is very difficult to wrestle with and that just turns off people who want to just "plug and play". I've lent my Boses out to four different friends over the years and they love them dearly. Of course then they listen to my v4 and are blown away with what they've been missing.
The rear LFR drivers enforce the "Early Reflections" curve. When this curve is brought up closer to the level of the Listening Window, magic happens! You get an enormous sound-stage and wrap-around with virtual images to die for. It's not as simple as just slapping on some rear drivers though. The front and rear drivers have to work in concert across the mids otherwise you get attenuation in the response. Bose knew that too. That's why his "free space array" at the top of the 601s has multi-directional tweeters yet a mid-range that points forward. He could not control mid-range reflections using analog means so he chose to reflect highs only.
Like you say, there is a delay somewhere but I can't be sure where or how much. I say that because those rear drivers are also reflecting off the front wall. To understand where you need to add a delay and how much that delay should be and for what frequency range(s), you really need to characterize loudspeaker behavior all the way around. Then you look at the curves and decide what you need to boost, what you need to attenuate, what delay needs to be added and of course that is some of the secret sauce right there. The DSP makes implementing all that so easy.
Here's the poem sung to the tune of "We Three Kings from Orient Are". This is my interpretation of the spinorama from stuff I've read mostly from Floyd Toole:
We six curves of Axiom are
30 years old we've come so far
every one eighteenth pi rad, an anechoic curve we add
of spinorama data not scalar.
O curves of tone and SPL
curves with similar shape and flare
gentle slope, low Q nope
perfect sound these curves foretell.
Direct sound real flat without any gain
"Axial Response" that is my name
simple content, most important
over all curves I reign.
A "Listening Window" nine curves mean am I
0 to +/-30 degrees across, 10 degrees down, 10 degrees high
within a dB, these curves must be
for listeneners to joyously sigh.
Image width, stability, timbre to tame
+/-40, 60, 80 across and 50 down and high's the game
most that we hear, bounce from quite near
"Early Reflections" is my aim.
A speaker's signature doth we take now
weighted mean of 70 curves is how
downward tilting, no broad wilting
"Sound Power" curve art thou.
The "DI" curve is the cash cow
the "Listening Window" from "Sound Power" take away now
closer to zero, it's a hero
listeners will procalaim a big "Wow!"
One last curve is for finesse
"Early Reflections" from "Sound Power" we minus
lateral prophylaxis, from far-off axis
"Early Reflections DI" shows polar bias.
Low DI with curves smooth and similar
disperse the sound as not to be insular
audio pornography, via sonic holography
sharp images spaced out renders them singular.
Axiom's direct radiators sound great when they're played
sound power declining 3dB per decade
if that DI, is a bit high
constant, low DI LFRs can be yours via trade.