I am not an audio engineer and may not understand this fully, and this is from many years ago, but my understanding is that greater bit depth translates to greater dynamic range. With digital volume control the signals dynamic range is compressed in the digital domain (effectively reducing the bit depth of the source) and brings the audible information closer to the noise floor - when you run this signal to an amplifier after the conversion the noise is also amplified and can become audible.
This is why, as I understand it, that doing digital volume control (back in the day) could degrade the sound and that you should do volume control with high quality analog gain after the signal was converted, and why you should feed your pre-amp/amp at full line level.
One way around this, is for the dac to upsamole the incoming signal to a higher bit rate before applying digital volume control and converting the signal to analog - this helps preserve the separation of the sound we want (music) from the noise we don't want - when processing in the digital domain.
But if you are not doing digital volume control - the extra bits don't matter (at least for this reason) because 16 bits provides plenty of dynamic range to cover what we can hear, while keeping the noise below audible levels.
If I've got this wrong, someone with more knowledge and understanding please clarify!