Quoting @tomic601 (replying to my post that rear-firing tweeters can correct the spectral balance of the reflection field) :
"While destroying the timing information that the ear brain is much more sensitive to. "
There are conditions under which a rear-firing tweeter can can be detrimental. Imo we do not want the output of the rear-firing tweeters to arrive too early nor be too loud, and we want its power response to be correct for the application. These characteristics are perceptually intertwined. Hence the "implemented correctly" stipulation in my previous post.
@tomic601’s follow-up post:
"my decision references are unamplified acoustic instruments in reverberant spaces captured w simple microphones, so the temporal data is in the recording."
Imo effectively presenting "the temporal data in the recording" is precisely the scenario in which a correctly-implemented rear-firing tweeter is most beneficial.
You see, in the playback room there is a "competition" between two sets of spatial cues: The venue spatial cues on the recording, and the "small room signature" inherent to the playback room. It is desirable for the venue spatial cues on the recording to be perceptually dominant if the goal is a "you are there" presentation.
Painting with broad strokes, the ear judges the size of an acoustic space by three characteristics: The time delay between the first-arrival sound and the first reflections; the temporal "center of gravity" of the reflections; and the decay of the reverberation tails.
It is in the effective presentation of the reverberation tails on the recording that a well-implemented rear-firing tweeter is most beneficial. Briefly, the in-room reflections act as "carriers" which deliver the reverberation tails on the recording from all around.
The ear looks at the spectral balance of incoming sounds to judge whether they are reflections or new sounds, and the overtones are especially critical to the ear making this determination. If the overtones are not loud enough for the ear to correctly identify the reflections as such when delivered by the in-room reflection field, that energy ceases to be "signal" and becomes "noise". But if the overtones are still loud enough, the ear will hear the reverberation tails arriving from all around as they decay, delivered by the spectrally-correct in-room reflections. This spectrally-correct delivery of the reverberation tails by the in-room reflections effectively presents the natural decay characteristics of the reverberation tails on the recording, which in turn are a significant contributor to a "you are there" playback experience.
And a well-implemented rear-firing tweeter corrects the spectral balance of the reflection field, restoring its typically-too-weak overtone levels, without introducing other problems.
That being said, this is a complex topic and this post is an incomplete look at just one aspect of it.
Imo and ime.
Duke