I can always hear class d amplification because it is so tonally off that it is like fingers scratching on a chalkboard to me.I just listened to a class D yesterday that was more focused and just as relaxed as a good tube amplifier. So I very much doubt this statement- it is trolling IMO.
Class D is used in most powered subs which is not to say it can produce high frequency well.This probably depends on what is meant by 'very well'. I listened to two amps yesterday, one tube and one class D. They both have less than 1 degree of phase shift at 20KHz. The class D amp has over an order of magnitude less distortion than the tube amp at that frequency. But its primary distortion product is the 2nd harmonic, and enough that just like a tube amp the 2nd is able to mask the presence of the higher orders. So it sounds like a tube amp, although considerably more neutral owing to lower distortion overall and the ability to act like a nearly perfect voltage source.
But not all class D amps are like this. They have as much variance from model to model and brand to brand as you see in tube amps, which cover the gamut of SET, OTL, push pull triode, push pull pentode and so on.
The bottom line is you have to be careful about making blanket statements; in the world of class D as in almost any other topic blanket statement are so general as to be rendered false.