it doesnt matter if you achieve attenuation by dividing the 16 bit level component of a stream of samples or by using a resistor as a voltage divider.
This is the part where I'm not following. In my head, if you're using analog hardware of sufficient quality, you can attenuate the signal to be very quiet, but still preserve it's dynamic range. In fact, the DAC is already outputting a very weak, but faithful analog reproduction of the signal, and an amp with a decent S/N ratio is able to bring that very weak signal up to a listening volume without introducing enough noise to matter.
Hypothetically, if for some reason, you took the signal post-amp, used a pot to attenuate it again down to the energy of the post-DAC level, and again ran it through another amp you would theoretically have the same signal still (I understand that in the real world we would start amplifying noise and the signal would degrade, but stick with me). Nothing about the process necessarily introduces noise and thus destroys the signal, you're only limited to the quality of the components at that point. If you had an infinite chain of theoretically perfect amps and pots, you could repeatedly attenuate and amplify the signal forever without ever losing any quality. It's an analog process that theoretically preserves the signal, +/- some amount of error due to physics.
Meanwhile, 16b is 16b. If you start shrinking all samples relative to each other (ex. down to 1/64 the original volume, or 10b of resolution), different values inevitably have to clamp to the same values (fitting 64k values into 1024 values), losing information and resulting in poorer quality. If you then try to send that 10b signal through a DAC/amp to achieve the same listening volume that you would have had before digital attenuation, it's just a 10b signal bit shifted up. All your LSBs are 0s. You can't possibly attenuate digitally, and then amplify it in any way and hope to get the same signal back. It's a discrete math process which destroys the signal by design.