There are other things to consider, even when assessing square wave response vs. music:
- If an amp has "overshoot", or it takes the initial transient beyond the original wave's amplitude, then you may get a sound that is harsh or overly etched. Upon hearing this type of sound, some listeners may be impressed, as the amp sounds "fast", and "detailed". However, over time, fatigue sets in, leading to increased sales of used equipment online.
- Similarly, if an amp exhibits a type of "ripple" on the trailing end of the wave, then there could be phase anomalies. Imaging may suffer, or there could be a 'disjointing' between high and low frequencies, causing a smearing when both are present. I think when an amp does this, it causes the music to run together, and makes the quiet moments between notes noisier.
- The best amps are not just the fastest, but are uniformly accurate in terms of frequency AND phase across those frequencies. By responding quickly and releasing just as quickly, the amp lets the music sound like music, and the spaces in between sound as they are supposed to: silent. Ironically, this is how a really "fast" amp can make the music sound SLOWER: "unrushed", and can contribute to a sense of rhythm, pacing, and overall musical enjoyment.
This debate has been around since the 1970's at least, when Kenwood marketed its line of "high speed" amplifiers. Sorry for the long response, but I just wanted to clear up the subject as best I could.