I personally avoid digital volume control as it's lossy.
That depends on the implementation.
It is correct that a volume reduction of about 6 dB costs 1 bit. If a 16-bit CD has a dynamic range of 96 dB, then a digital volume control could loss of informations.
The reality is that digital volume controls known to me, such as Roon or HQPlayer, extrapolate the music to 64Bit beforehand. That is not a problem and also lossless. In this way, any volume control can be implemented without losses. And that has advantages: for example, there are no channel inequalities and no channel crosstalk.