Actually, Class D amplification has nothing to do with the power supply smoothing (sometimes called filtering) caps. The whole capacitor size question in this thread is all about linear power supplies.
The objective of the power supply in an audio amplifier is to convert the mains AC current (120v/60Hz) to DC current at a desired voltage level. The power transformer changes the voltage level, while a full-wave rectifier converts the alternating current to direct current. Rectifiers aren't perfect, so the output current still has residual AC "ripple" in it, and what the capacitors do is smooth the voltage ripple. The size of the capacitors are indicated by a formula which includes the voltage and the magnitude of the ripple. Power supply capacitors do not determine the level of power delivered to the amplification stages; that's all up to the transformer. There is no benefit to making the capacitors larger than necessary to smooth the current to DC, as proven in section 8.1 of this article:
ESP - The Audio Pages. Linear power supply design information - Learn how to design your own high performance amplifier power supply.
sound-au.com
I think
@PENG and I have posted it multiple times. Required capacitor size depends on what the desired DC voltage is and what the maximum current will be from the power transformer.