The discussions on this thread are vacillating between:
a) dynamic range in the music itself
b) dynamic range in the recording you are playing, and
c) dynamic range your system is reproducing
So, when we discuss correlation between DR and genres, we are on a) above. Certain genres of music are low on DR and suited better to background listening. Some other genres are high on it and compel your to pay attention.
However, there can be exceptions to the above and what matters is the DR in the specific music being being played. Now, this is where discussion b) comes in. All the mixing/mastering/remastering et al that the sound engineers do on the music can either keep the DR in the original piece intact, or reduce it down. This is where the ‘loudness war’ happened. Now, those who have ears/systems that can discern compression wouldn’t usually like DR reduced in this fashion, even if they prefer low DR genres as above. Well, unless you are interested in the loudness too - boom box/parties for example.
And then we get to what kind of speakers and systems produce the music on the record/stream without further compression (discussion c)). Yes, usually high sensitivity speakers do a better job here. But I am not sure if sufficiently amplified low sensitivity speakers won’t (ATC comes to mind). Lots of factors, including the room can affect the DR you actually listen to. And a lot of effort we put on optimising our setup usually goes in preventing further compression.
That is how I understand the thread and the subject now. There can be of course technical imperfections in the above as I am a lay listener. And would be glad to learn from.
Personally, I’d like the best (highest) possible DR in all the above a, b, and c, whether I am listening intently or in the background. It just feels more lively. If I want to do an activity where I don’t want to be distracted, I’d not put the music on. But that’s just me. I can understand those who’d like soft music played in the background like in an elevator/restaurant. I do dig it too, but not from my system. Speaking of system, my main system (a budget setup) has limitations in producing the DR in the recording (c above). However it’s a compromise I have settled for. I could probably get higher DR through more powerful class D amplification in same budget, but then I might lose the tonal accuracy (I know that couid be debated by some, and I hope D class improves soon to the point where it’s not an issue - so much more economical and green that’d be). My desktop (headphone) system however, does a much better job of the dynamics.