Integrated Amps Vs. Pre-Amp + Power-Amp

Why is it that having the volume control in the preamp is so popular? I would have thought that a control in the Power-Amp that varies the gain of the amp rather than the amplitude of the input signal would produce a better sound output....... what i mean is that by changing the gain of the amp and not the amplitude of the input you keep the signal well above the noise floor ..... Why is this not done more often?
Everything changes with the amount of NFB you use.
Soundstage, musicality, stability, spectrum of distorsion etc, etc......
Even as little change as 1dB is clearly heard (if you have a small amount of NFB), and substitute the volume control with a variable NFB would need a range of approx. 0 to -64 dB.
Even if it is possible to make a working solution the sound quality would change too much with the setting to be acceptable.