Yup, but it can be achieved by taking a slightly different approach... I don't necessarily strive to accurately 'recreate the original sound', because as you correctly say, none of us knows what that was, including me.
What I do instead, is strive for my system to (as far as possible) accurately reproduce the sound of real instruments and voices, as dictated by my own ears and judgement, and crucially from my experience of listening to live (un-amplified) examples of such, whilst attending various music performances over the years.
That experience allows me to judge how things are supposed to sound, and therefore acts as the benchmark I use to 'tune' the musical presentation of my system, via judicious component, cable and speaker selection.
For me, therefore, it doesn't really matter whether I've succeeded in accurately recreating the original sound, as long as to my ears, my system has succeeded in faithfully recreating the sound of a piano, or the sound of a drum or guitar, so that it sounds convincingly like such, and not merely a poor facsimile. *That* is what hi-fi is about, and in that respect, the fact is some things aren't meant to sound 'nice'...
I can also say with some conviction, it's a process that works very well indeed, if you get it right!
Marco.