Photographers do this a lot. They think that if one quantity is bigger than another, then the other one kind of goes away.
We see the same fallacy in sharpness discussions.
Indeed, but one should also avoid the opposite mistake of pursuing perfection in one respect (like minimizing quantization noise) at the cost of ignoring faults in other respects (the greater imperfections of higher levels of analog gain, like amplifier nonlinearity and clipping). I have perhaps given the wrong impression that I support the dogma that "more that unity gain is pointless", so let me clarify:
At some ISO speed setting (seemingly in the range 400 to 800 with many good current sensors) the analog gain brings the noise level entering the ADC up to the noise level then caused by quantization in the ADC: I believe that this is what some call "unity gain". Contrary to the above dogma, I see that it can still help to amplify a few stops beyond that, so that the noise floor in the incoming analog signal is at about two or four times the quantization noise, but beyond about that, quantization noise is insignificant, and reducing it further with further analog gain is of no practical value. Indeed, digital gain in raw conversion becomes a better approach: it is perfectly linear, and one can back-off from clipping – which I suppose is then more accurately called "arithmetic overflow".
To quantify: describing the ADC quantization noise as of level 1 (a 1 bit error?), if the noise in the input signal is amplified to be two stops higher it is at level 4. Then the combined effect in the deepest shadows is the RMS combination sqrt(1^2 + 4^2) = 4.12, so raising the deep shadow noise floor and lowering the total engineering dynamic range by 0.04 stops compared to what one would get by avoiding ADC quantization noise effects entirely. This I would call measurable but in practice negligible.
Raising the ISO speed by one more stop, to three stops over unity gain, the noise floor in the amplified analog signal is at eight times the quantization noise floor, and the quantization noise raises that total noise from 8 to 8.06, a change of 0.01 stops, so a tiny 0.03 stops better than the previous "two stops over unity gain" case. If the cost of this 0.03 stop improvement in the deep shadows is the risk of clipping the highlights one stop earlier . . .
P. S. In all but the deepest shadows, photon shot noise overwhelms these other noise sources anyway.
TL;DR Pardon all the numbers: my point is that these numbers are negligible, and we should not obsess about pushing up the analog ISO speed gain in pursuit of perfect ETTR histogram placement in low light situations! Good modern sensors often let us use any ISO speed in a safe range that avoids the problems at either extreme, so we can think more about composition instead of worrying about absolutely perfect light metering and settings choices.
