Class D amps can be engineered to be a perfect circuit. However, you must include the speaker impedance itself as part of the circuit. A Class D amp can provide perfect frequency response if the speaker is a very constant impedance (i.e. like a straight 8 ohm resister). However, a real speaker is almost never a perfect resistor and its impedance curve is typically all over the place (such as ranging from 3 ohms to 16+ ohms in different frequency areas). Some speakers are harder to drive with a Class D amp. In these cases, the speaker itself tends to drive the frequency response of the Class D amplifier and you get things such as tube-like midrange, weak bass/sub-bass, less punch/slam, high frequencies rolled off. A regular Class AB amp will still be affected by the speaker impedance curve, but not nearly as much (this is a significant difference). I played with Class D amps for a while until I figured all this out.
Sure, the Class D amps will run very low heat and are very efficient (and they are very small), but if you have hard to drive speakers, a normal Class AB will always be superior. I had some Focal speakers that are very easy to drive and they worked well with Class D. However, when I moved to B&W 805 Diamonds, they just did not do as well. An Emotiva XPA-1 monoblock just stomped all over the Channel Island Class D. (yes, I do understand that the Emotiva is a much heftier amp, but still high-current Class AB).
I’m not sure what advances have been made in Class D over the years, but I would really keep this in mind if you want to research and try Class D. In my opinion, the B&W 805s that you have can really sing, but they really need a high-current Class AB amp (which does heat up in any amp you choose). If you do choose Class D, I would suggest you mate it with a speaker that has an almost constant impedance curve.