It seems to me that testing square waves evaluates transient response. The maximum rise time produced by the amp is linked to frequency response, isn't it? There is always some ringing after the transient, and the frequency of that is important, too. So, can we hear a qualitative difference between a square wave (with the fundamental low enough to be hearable) through amps of different frequency response and rise-time capability, into various loads? Square waves, of course, have an unlimited supply of available overtones, so if frequencies above 20 KHz affect the sound of frequencies below 20 KHz, then we ought to hear the difference. It seems to me a square wave represents the fastest theoretical rise time.
Rick "always looks at square-wave shapes and transfer accuracy when testing provides it" Denney