IMHO, one of the biggest problem with consumer audio equipment is that the power supply cannot supply the peak power requirements of music when driving headphones at high levels, and as for transients there's insufficient energy storage in the power supply, and battery operated devices have insufficient voltage overhead to drive peaks cleanly.

Most cheap headphones are relatively insensitive, and can be quite high impedance, so need the volume cranked up to be useful making the problems worse. A good pair of sensitive headphones allows the volume to be kept down and thus give the audio amplifier and its power supply the best chance to provide a clean signal.

However, I've not done any analogue electronics for a while, and now it's all class D/PWM switching amps, I might be completely wrong