Tangential fun fact: amps have a fixed gain, because it's hard to make a variable gain without distortion [1]. The volume knob doesn't control amplification, in fact it controls an attenuation stage, because it's easier to make variable attenuation with low distortion.
[1] that's why there were so many different "classes" of amps, they're all making different tradeoffs about how they're doing the amplification.
According to Claude, the attenuation stage is before the power amp stage. Does that mean worse SNR whether the volume is controlled using the volume control or via the input?
(Ignoring the additional quantization issue with a scaled digital input.)
You could put the attenuation stage after the power amp stage but it would require big beefy resistors that could absorb a lot of power. They'd get hot and the whole thing would be very inefficient.
[1] that's why there were so many different "classes" of amps, they're all making different tradeoffs about how they're doing the amplification.