I was looking into arcs g/h a while back. Linear power chimed in on the topic.
Class G/H has its issues, two main ones really.
1. There has to be a peak detect circuit to tell the amp when to change voltage rails, the problem with this is that there is no detection circuit with a high enough slew rate (speed) to swap voltage rails quick enough(it would have to be virtually instantanious) to respond to dynamic peak musical information so what happens is the peak musicical information gets clipped off before the amp can switch to the next voltage rail to supply the needed power to reproduce the dynamic peak.
2. As you approach the limits of the first voltage rail distortion increases, when it is swapped over to the next rail the distortion is lowered until you near the maximum of the next voltage rail and distortion starts to be increased again. This is almost always noticable and un-natural.
The idea of Class G/H was a good idea to increase the efficiency of a Class A/B amp but it does mess with the SQ of the amp, and that was the whole idea of staying with the Class A/B design was to still have better SQ than Class D. Class G/H is trying to minimize "power under the curve" by tracking rail voltage as close to the signal and not have as much wasted voltage not producing the music, as this extra voltage has to be dissapated as heat if not used to produce the audio signal.
There is a give and take, or compromise in electronics, you don't get something for free. The trade offs have to be analyzed and determine whether the gains out way the losses.