Well, I don't know. I mean what's more demanding as far as power requirement? The tweeter and midrange require a lot less power (I heard 10%) than the bass. And the bass is where you typically see the minimum impedance dip and wide phase angles.
BTW, who came up with the idea that high frequencies anomalies were associated with class-D amps?
You are correct that the bass does indeed require more power. So, if the amp were under-powering the speakers then that could explain the problem. BUT, that would not be a problem inherent with Class D topology but rather a problem of too little power (ie trying to drive the amp beyond its limits). Too little power can be a problem with ANY class of amp.
I'm sorry, I should be more clear and precise with high frequencies and Class D amps. Problems with the high frequency response WAS a problem at the birth of the class D topology. As far as I can tell, MODERN Class D amps have over-come those problems that the first few generations of class D amps suffered from.
So, HISTORICALLY there were problems with class D reproducing the high frequencies. Since Class D are "switching amplifiers", the "switching" needs to be orders of magnitude quicker than the highest frequency (20kHz), and it took a few generations of designs to get that figured out.
As far as Class D amps having problems reproducing bass (low frequencies), that has never been an issue associated with class D. Furthermore, class D amps are very popular in the car audio community and in the SPL competitions (driving subs).
On a side note, I'm danged interested in those new NAD Master Series that AH just announced. They are using Hypex nCore amps!