There is a common digital volume control chip, used in my McCormack MAP1 six channel preamp, which does 1/2 dB steps. It is a stepped attenuator, and no motor is involved. If such a chip follows the D/A conversion no bits are lost. If an analog output is being produced there is no reason to use another implementation.
Now, if you want to have a digital output and attenuate the signal there will be a loss of resolution. No matter how you process the data a 12 bit output obviously has less resolution than a 16 bit output.
Now, if you want to have a digital output and attenuate the signal there will be a loss of resolution. No matter how you process the data a 12 bit output obviously has less resolution than a 16 bit output.