Since recorded/reproduced will never be like live music, in the end it's just a matter of creating an illusion, or something that reflects it as best as possible.
After all, the title of Dr. Toole's book is:
Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms
It's about reproduction and not live music.
The most reasonable starting point should be to get it as close as possible, but really there is nothing that says you can do it any other way. Color the music heavily, for example, and this illusion of live music appears. Intuitively, I think it's a backwards approach, and besides, this coloring can appear to others (most?) as a bad approach to reflect live music.
From Wikipedia about HiFi:
High fidelity or hi-fi is a way of describing a very good home music system. "High fidelity" means that the sound is as close to the original as possible with no changes or added noise.
simple.wikipedia.org
As close as possible, no changes or added noise. Doesn't sound like coloring is preferable, quite the opposite.
But having said that, there is nothing that prevents colouring, seasoning as desired. I do that myself when I listen to old hard rock, heavy metal. I add bass because I think many of the old recordings are so bass thin.