From
https://www.pnas.org/content/97/22/11773 :
"The anatomical and biophysical specializations of octopus cells allow them to detect the coincident firing of groups of auditory nerve fibers and to convey the precise timing of that coincidence to their targets. Octopus cells occupy a sharply defined region of the most caudal and dorsal part of the mammalian ventral cochlear nucleus. The dendrites of octopus cells cross the bundle of auditory nerve fibers just proximal to where the fibers leave the ventral and enter the dorsal cochlear nucleus, each octopus cell spanning about one-third of the tonotopic array. Octopus cells are excited by auditory nerve fibers through the activation of rapid, calcium-permeable, α-amino-3-hydroxy-5-methyl-4-isoxazole-propionate receptors. Synaptic responses are shaped by the unusual biophysical characteristics of octopus cells. Octopus cells have very low input resistances (about 7 MΩ), and short time constants (about 200 μsec) as a consequence of the activation at rest of a hyperpolarization-activated mixed-cation conductance and a low-threshold, depolarization-activated potassium conductance. The low input resistance causes rapid synaptic currents to generate rapid and small synaptic potentials. Summation of small synaptic potentials from many fibers is required to bring an octopus cell to threshold. Not only does the low input resistance make individual excitatory postsynaptic potentials brief so that they must be generated within 1 msec to sum but also the voltage-sensitive conductances of octopus cells prevent firing if the activation of auditory nerve inputs is not sufficiently synchronous and depolarization is not sufficiently rapid.
In vivo in cats, octopus cells can fire rapidly and respond with exceptionally well-timed action potentials to periodic, broadband sounds such as clicks. Thus both the anatomical specializations and the biophysical specializations make octopus cells detectors of the coincident firing of their auditory nerve fiber inputs."
What does it mean? If onset of a transient is blurred over 1 ms or longer time interval, the transient may not be perceived the same way. Instead of startling or energizing, it could be boring, or simply perceptually dissipate within the rest of the music.
Compared to a good Class A, a good Class D amp isn't likely going to be more than 20-40 microseconds behind in swinging from zero to the full amplitude. By itself, this doesn't seem critical. Just 2% to 4% of the critical transient detection window width. Consider this a small timing distortion.
Yet in combination with certain loudspeakers, containing "heavy" crossovers and transducers that further blur the transient, such difference may sometimes preclude the transient detection mechanism from reacting, or at least make the transient subjectively not as loud.
If the high-end speakers designers were tuning their creations using "nearly-perfect" classic monoblocks, they may be stopping at a point when they can no longer detect the transient anomalies. Likewise, mixing and mastering engineers, listening to their nearly perfect studio systems, would make the transients sound right too.
Yet a less-perfect amplifier could theoretically push the overall system to a condition where the transient anomalies are heard again. Corollaries:
(A) A system with much less than perfect loudspeakers would exhibit such anomalies no matter what, and the difference between amplifiers in this regard may not be noticeable at all. Excessive DSP may lead to such situation as well.
(B) A system with "super-perfect" loudspeakers, and/or competent DSP, would in effect "tolerate" timing idiosyncrasies of different amplifiers, and thus the timing differences between such amplifiers once again would not be noticeable.
(C) Only when the loudspeakers, amplifiers, DSP, and the music are "off" just enough, the substitutions of such components could lead to noticeable subjective differences in transients. These differences can be further exacerbated by certain rooms acoustics.