I'm sorry you have to type so much, I am familiar with most of it, but I appreciate your effort to make sure we're on the same page without being a douche about it lol. It sounds like we're saying similar things, but I don't understand why lower precision is different from losing information. To me, that's the same thing, it's a lossy operation.
So the thing is, I have a pair of desktop speakers without any physical volume control that I primarily use for convenience. And for whatever reason, a comfortable listening volume with them is between 1-8% in the OS volume control. I guess the internal amp is just hardwired to be way too loud?
Anyway, I assume that this setup is resulting in objectively lower quality output than if I were to have a 100% signal going to a decent quality DAC/amp with analog volume outputting to the same speakers. And not in a "technically" kind of way, but in a very real "we just crushed the signal into 1/25th of its original scale" way. Would you agree? Am I mistaken?