Power is Voltage times Current.
Writing Current or Power at a given Impedance comes out to the same thing.
Class A is a topology.
To help Class A’s miserable efficiency, they often run relatively high voltages. Combine that with low capacitance (= faster response) to get more “slam”.
The PSU argument:
While linear PSUs might have huge output caps, Switch Mode PSUs have those huge caps on the input side. Linear Regulators due to their working principles are slow. So a load transient will drag down the linear PSUs caps which will then have to recover slowly, see Bottom of Page 2 for example.
A modern SMPS will do that in roughly a quarter the time, Bottom of Page 6.
Time scales on both are 10uS per division.
(There is a reason computers use switching regulators instead of linear for CPU and GPU power regulation)
More detailed writeup on amp classes here.