Think we posted at more or less the same time Dave
Why would it attenuate input signal? Sounds like bad way to do it,it will degrade the signal SNR and there is attenuator at the output of amp anyway.
The first part is true and your observation is correct, but it is all a mater of degree. If you use a volume control on an audio signal of 1V, as I said, the noise on quiet volume settings is acceptable.
But there is another aspect and that is called headroom. An audio signal, with music, not speech, has a tiny average amplitude, interspersed with huge peaks. If you have the level set too high the amplifier will not be able to reproduce these peaks with the result that your music will loose some of it's brightness and sparkle.
Not sure why you think there is an attenuator on the output of the amplifier.
I also saw many measurements of amps and often the amp have lower THD+N at same output power when set to lower gain,that suggest to my noob brain that something more complex is happening inside the amp when changing the gain setttings.
Nothing is altered inside the amp. The volume is changed by a pot just like I said. An amplifier nearly always produces less distortion at low levels (this is not absolutely true for all amps but in principle it is) because the components in the amplifier are not been stressed so much. Think of it like a car, at slow speeds it makes little noise but at high speeds it makes a lot of noise. But nothing is changed inside the car.
Doesnt it change the internal power supply voltage to the output stage transistors?
Unless the amplifier has a stabilized power supply, or it is a class A type, the voltage power rails are changing all the time. They drop when the amplifier is producing a loud sound because the amplifier takes more current from the supply line. Then when the current demand is reduced for a quite passage of music the supply line raises again.
The power lines have no effect on the volume from the amplifier, because amplifiers use negative feed back and that keeps the gain constant. The only time that the supply lines will affect the sound is if the amplifier is being driven with too large a signal and it is clipping (not reproducing the top and bottom extremities of the output waveform).