Quoting Doug Self:
"Sinewaves are steady-state signals that represent too easy a test for amplifiers, compared with the complexities of music."
This is presumably meant to imply that sinewaves are in some way particularly easy for an amplifier to deal with, the implication being that anyone using a THD analyser must be hopelessly naive. Since sines and cosines have an unending series of non-zero differentials, "steady" hardly comes into it. I know of no evidence that sinewaves of randomly varying amplitude (for example) would provide a more searching test of amplifier competence.
I believe this outlook is the result of anthropomorphic thinking about amplifiers; treating them as though they think about what they amplify. Twenty sinewaves of different frequencies may be conceptually complex to us, and the output of a symphony orchestra much more so, but to an amplifier both composite signals resolve to a single instantaneous voltage that must be increased in amplitude and presented at low impedance. The rate of change of this voltage has a maximum set by the frequency response and amplitude capability of the channel and is not generally greater for more complex signals; you do not get hgher slew rate with bigger orchestras. You must remember that an amplifier has no perspective on the signal arriving at its input, but literally takes it as it comes.