Part 1: Is that "Live" sound a key reference against which an ambitious system should be judged?
Part 2: How is an actual "Live" performance different, in a technical sense, from what most home systems can reproduce?
Part 3: Is "Live" sound even worth chasing? What happens when the dog catches the car?
First of all, we have to define what is "live" sound.
Even in big concert hall different seats will have different sound. And conductor's place will have one another different sound.
So, I'd prefer to tell about reproducing dynamic sound field of a (sometimes live) event. This in principle possible in stereo only if that event was recorded by dual-mic or any other puristic technology when sound was directly converted into record without intermediate dynamic sound field.
Otherwise we shall reproduce last dynamic sound field that was approved by producer or band or someone else.
I've been once in special diffusing room, which was built around system for correct creating an illusion of being somewhere near orchestra. Worked well on some dual-mic Decca and DG CDs with good scenery and imaging, but most modern multitrack records are very ... artificial and fuzzy. So, transfer function of this room+system was optimized for some specific tracks.
For correct reproducing sound field we have to optimize transfer function somehow. This can be done right only for some records, because mics are different, control rooms are different, mastering engineers are different, etc.
So, my opinions about your questions are
1) at some degree, not completely, because we have some constraints like SPL in room due to laws, for example.
Also, if we are really ambitious, we cannot optimize transfer function 100% correctly unless we have recorded exact this CD and know original event. So, there must be some averaging and error and we have to accept this, otherwise it's a chase for ever changing goal.
2) dynamic range, size of room and size of sources, RT and a lot of smaller differences
This can be partially imitated (big speakers with high DR and SPL, for example) , but not completely. Room size and RT is main trouble.
3) if you need good fidelity, your transfer function optimization will be seriously limited to some tracks. A lot of other records might suffer.
So, i'd not go extremely deep unless your tastes are also limited.
Personally my preference is "good enough" emotional message translation. I accept the fact of illusion itself and don't care much about live sound.