Micah,
There is nothing new about class H (or class G) amplifier designs (they are similar), which have been around since the late 1970s. The first class G design I recall was developed by Hitachi. It used two voltage rails, a lower-voltage supply for lower power output, then, when music signals became large, the amp would momentarily switch to a high-power voltage rail and a second set of output devices. A class H design is a variation of class G, and uses a power-supply input-tracking circuit, so on peaks the power supply delivers enough voltage to allow the amplifier to briefly deliver much more current to handle the peak without clipping. In both class G and class H, the amplifier runs cooler so long as signal levels remain small.
Class G designs were never that popular in home audio because it was feared that the voltage-rail switching would add distortion when it switched to the high-power output devices. Both class G and class H are quite popular in professional applications.
Incidentally, there are not "problems that come with most digital amplifiers"; properly designed digital amplifiers have many advantages, however, they tend to be relatively expensive.
No amplifier design is perfect, however. Each amplifier class has distinct advantages and disadvantages.
Regards,
Alan
