OK, after a bit of thought I think I see what you are trying to say with the analogy. It helps me to think of it in terms of arithmetic. If you start out with 16-bit audio you have 2**16 different peak-to-peak voltages available. If you reduce the volume by 12 dB you then only have about 2**14 available voltage steps, which is perhaps where the don't-go-below 75% maxim comes from (75% being about a 12.5 dB cut in .5 dB steps.) So don't go below 75% or you playback sounds like an old 14-bit CD player!
But most digital volume controls these days are 24-bit or 32-bit. The Squeezebox outputs 24-bit words, and shifts 16-bit audio to the most-significant bits of each word. This doesn't magically give you 24-bit resolution, but it does mean that with a 24-bit DAC you retain at least 16-bit resolution even with a quite large attenuation (theoretically 8 bits or about 48 dB; but that's nearly the full range of the volume control). Even with 24-bit files, I wouldn't worry until the attenuation was more than 24 dB (or about 4 bits) since you can't really expect to get more than about 20 bits of resolution anyway.
But most digital volume controls these days are 24-bit or 32-bit. The Squeezebox outputs 24-bit words, and shifts 16-bit audio to the most-significant bits of each word. This doesn't magically give you 24-bit resolution, but it does mean that with a 24-bit DAC you retain at least 16-bit resolution even with a quite large attenuation (theoretically 8 bits or about 48 dB; but that's nearly the full range of the volume control). Even with 24-bit files, I wouldn't worry until the attenuation was more than 24 dB (or about 4 bits) since you can't really expect to get more than about 20 bits of resolution anyway.