Why is it that performing musicians typically want a 'live' room to perform in, and audiophiles strive for a 'dead' room and go to all sorts of trouble to minimize wall reflections?
Very wide open question. My take on both is that there are a hundred shades of gray.
For instance: I have heard music in a certain venue where there quite a number of these very, very large absorptive panels decently far up these rather tall walls, which can be folded closed. Depending on who is performing or rehearsing in there, they take this really long pole, and either close them (reflective) or open them (absorptive). They may only choose to leave some open and others closed.
An extremely reflective venue, say a cathedral, might be really great for an a cappella ensemble of 4 vocalists (think Hilliard Ensemble), but probably be a nightmare for certain symphonic works (think
subito changes of dynamics and texture, where any starkly differing previous passages are still ringing through into the next passage; does the conductor then choose to take abnormally long pauses between every differing passage?).
For the audiophile, I believe it is a matter of application as well. For instance, if there is added ambiance from the room on top of what is already recorded, it could possibly be indistinguishable, IMO. However, for certain HT-audiophiles, an outfielder encouraging a teammate in a baseball movie, or a car screeching around a corner in a chase movie, or a spaceship blowing up an alien in a sci fi flick, none of those really benefit from a "living room ambiance". This same ambiance however is rather familiar to us with a kid practicing piano, a string quartet performance, what have you.
But even for say a classical music lover, if one has speakers with superb off axis performance, with decent positioning, many would say you would actually be better off without sidewall absorption, as the reflected sound would be similar enough to the direct audio, where it can successfully give you a wider stage. Poor off axis response, OTOH, might mean that it's not worth the compromise, because the reflected energy is so dissimilar to the direct audio, it has an overall destructive effect.
Then: let's say everything above is groovy. But that you are backed up, on a couch that is backed up right against the wall. Your otherwise perfect audio is probably ruined simply from a bad choice of listener positioning. Some people will use absorption in this case; it's a matter of application, and/or compromise.
Another compromise-application: Good speakers, overall good acoustics, even good listener position, but say the left speaker is very close to the left sidewall, where the right is totally open into a very large room. The audio will simply be lopsided in energy due to the boundary effects, and broadband absorption could possibly mitigate any such issue, even out the compromise if you will.