You are certainly right with your concerns purely mathematically. HOWEVER, within a factor of 10 I would argue it is inaudible.
I have no idea what you are talking about, what 'factor of 10' are you talking about.
There is also data reduction at the pre-amp volume control = signal attenuation/reduction.
Data reduction implies you are speaking of the digital domain, it certainly does not happen in analog.
Next, the worst culprits are the speakers, particularly with respect to loss of. resolution.
What's your metric for 'resolution'? If some thing is lost it must in in some quantifiable amount.
Then there is Fletcher Munson to consider, so brain processing.
Maybe you could rephrase that in a complete thought, or at least a complete sentence.
Accordingly, the digital volume control "argument" is a red herring.
No.
Re dynamic range, that is the ratio of loudest to quietest. Whether it is or 10,000:1,000 or 5,000:500, that is the same ratio, same range. Within reasonable limits, dynamic range is independent of volume.
Dynamic range is gated by the noise floor, whether of the electronics or the listening environment on the lower end and by the power and/or acoustical limits of the system on the upper end, so the dynamic range of the system as a whole is entirely dependent on volume. To achieve a playback dynamic range of 60dB requires a very quiet room (50 dBa or less) and a system peak output of 110dBa. To reach full symphonic levels of 120dBa requires 10X the power, and a speaker system capable of that level.
For context a 2X8" tower speaker, pretty much regardless of manufacturer will have a maximum peak volume capability of around 112dBa. Thats around 150W with a speaker sensitivityof 90dB @ 1W/1M. A 5" standmount, like a KEF LS50, 104dBa, with a sensitivity of 84dBa and 100W maximum power handling.
Working the other direction, a normal listening level of 85-90dBa might only require 1 watt of power, but the system will run into the listening room noise floor at 45-50dBa limiting the dynamic range to around 45dB. So dynamic range is quite dependent on volume.
Don't worry that much, just happy listening.
The only time you might worry is with very quiet passages in very low res files. You *might* be able to hear a difference in the fade out of a pop song. For anything more real world, it is inaudible.
I'm afraid were going to have to disagree on you audibility claim. First, I'm way beyond 'worrying'. That said, truncated data is quite audible at normal listening levels between 80-90dBa. Second, your grasp on this topic is quite marginal.

