The EPC eGaN FETs switch 10x faster than silicon MOSFETs and have zero stored charge. I'm guessing that probably improves sound quality when used in a class D amp.While they are faster its incorrect to characterize them as having 'zero stored charge'. The gate (input) capacitance is the big issue; on traditional MOSFETs it can easily be around 2000pf, which requires a bit of current from the driver circuit to switch the device at speed. GaNs tend to have less gate capacitance (about an order of magnitude less, depending on the device) and that is part of why they can switch faster. But that gate capacitance still plays a role in the driver design.
Much moreso than actual switching speed, getting dead time down is what reduces the distortion in a class D amp. Many of the GaN devices switch fast enough that amps with zero dead time can be built at pretty close to current switching speeds (400KHz or so).