Much has been made over the phenomenon of “supply pumping” in single-ended class-D amplifiers (i.e. not a full-bridge output). Maybe it is an issue, maybe it isn’t, but it is very difficult to answer that question unless we have some numbers to work with! This is not the sort of thing you can simply listen to on your reference system and say, “Yes, now I’m sure of it: roughly 15V peak at 20Hz.” Well, maybe you can, but I certainly can’t.
This article derives the magnitude of the supply pumping in terms of known parameters of the amplifier: rail voltage, bus capacitance, load impedance and frequency. It shows that the only variable the designer really has control over for the reduction of supply pumping is bus capacitance, at least without resorting to more advanced methods, but adding more capacitance is the simplest and gives the best results by far.