You are simplifying this too much. You need to look at residual noise at the amplifier output as a function of volume control position considering residual noise and gain from the amplifier as well as residual noise inherent in your source.
If you don't have issues with audible hiss currently, adding an analog volume control is not going to help you.
Based on PMA's measurements ->
https://www.audiosciencereview.com/...s-power-supply-measurements.19507/post-642669 A07 residul noise is 10^(-75.2/20) = 174 uV residual noise from the A07 with an improved power supply. For reference this is a 5 W in to 4 ohm dynamic range of 20 x log[sqrt(5 x 4) x 10^6 / 174] = 88 dB.
Actual system noise performance will depend on the volume control position of the A07, lower gain = lower amplification of upstream noise but this comes with a channel imbalance penalty. For this analysis let's assume 29 dB gain like the ASR review.
Residual noise from D10S = 2 x 10^(-112/20) = 5 uV
Amplified residual noise from D10S = 5 x 10^(29/20) = 142 uV
Total residual noise from amplified DAC output and amplifier = sqrt (142^2 + 174^2) = 225 uV
225 uV residual noise is pretty good and is likely not audible depending on speaker sensitivity, hearing and listening position.
Now let's say you typically listen at -20 dB, that will reduce your output signal but noise remains constant with digital volume control.
Voltage at DAC output at -20 dB = 2 x 10^(-20/20) = 0.2 V
Voltage at amplifier output at -20 dB = 0.2 x 10^(29/20) = 5.6 V
Dynamic range at amplifier output at -20 dB = 20 x log(5.6 x 10^6 / 225) = 88 dB
Now let's look at the case of perfect analog volume control. In this case both upstream signal and noise are attenuated.
Attenuated residual noise from DAC output at -20 dB (analog) = 5 x 10^(-20/20) = 0.5 uV
Amplified residual noise from DAC output at -20 dB (analog) = 0.5 x 10^(29/20) = 14 uV
Total residual noise at -20 dB (analog) = sqrt (14^2 + 174^2) = 175 uV
Now noise is dominated by your amplifier where as before it was roughly equal parts DAC and amplifier.
Dynamic range at amplifier output at -20 dB (analog) = 20 x log(5.6 x 10^6 / 175) = 90 dB
You've gained 2 dB dynamic range at -20 dB volume position with a perfect analog volume control. Without a lower noise / lower gain amplifier you will not be gaining much from using a higher dynamic range DAC or an analog volume control.
Michael