You seem to know a lot about technical issues about class D Amps (I dont), but in my case I dont feel any of the problems you have mentioned above, if I understand you correctly.
When I listen to music at low levels at night (everybody is sleeping), I dont feel the mids or the highs rolled off or not involving at all. In fact, as the AC Power is cleaner and the ambience noise is lower, I experiment the best of the music as it gets much more involving, smoother, with more dynamics, detail, better tone and with an incredible soundstage.
Also, when I listen loud (I try not to do it often for my earing safety), I dont feel the sound harsh.
On the other hand, I've listened to multi thousand dollars systems (+120k), much more expensive than mine, and I've found them harsher and with more digital flavour than mine. And those systems had class A or A/B amps.
In fact, I've had class A valve amps that didnt sound as smooth and grainless as my class D amp, at all.
I dont want to start an endless and pointless discussion, but my experience doesnt follow your theory. I guess there must be exceptions.
My amp is a Nord Acoustics NC500DM with Rev D boards and Sparkos Op Amps. My preamp is the Audio-gd Master 1 and my DAC is the Audio-gd R8. I feed the DAC with the SOtM SMS-200 Ultra Neo going through the Gustard U16 USB to I2S converter. My speakers are the Q Acoustics Concept 500 floorstanders.