What is it I'm failing to grasp?

Almost all live shows I have heard were not something I could do all day. However, I can listen to my system all day and actually do. So, my system must not convey a real 'live' experience. That does not seem to bother me.

Today I cancelled my TV cable and replaced it with nothing because watching TV gives me stress of not listening to my system. If I watch anything, it is my hockey and baseball games on the internet with the sound off and the stereo tunes cranked.

Most live concerts of the popular variety--not classical-- are way too loud for me. I wear ear protection (cheap Etymotics are way better than the give-away foam plugs). And that can sound fatiguing. 

I remember hearing Etta James at Carnegie Hall a while ago-- Susan Tedeschi  opened, and though we had excellent seats, the sound was a blur-- she overplayed the room. Etta's band gets on and it's bliss.

I listen to a lot of so-called spiritual or soul jazz, mainly from the '70s. Much of it is decently recorded even if the pressings were made at the nadir of vinyl quality. I can get a very compelling performance at home but it will not scale to the level of King Crimson in my room- I did that comparison listening to Live in Toronto 2016 the morning after I heard them live in a 2,000 seat hall. Even with multiple woofers, I could not get the power of the bass, nor the sheer amplitude of the show at home. But, like the OP, I don't necessarily listen at crazy high db. Typically a little over 80db on peaks, "C" weighted. And it sounded very much like what I heard live. 

Is it the same as "live"? Nah. But it can be compelling, sound like real instruments particularly when the arrangements are spare. (I have thousands of classical records that I rarely listen to anymore, but keep anyway).

I remember one of the first systems I heard that could reproduce a full sized double bass-- it was a pair of those huge Duntechs from the '80s owned by a compadre who was a listening buddy. We shared many great listening sessions. At the time, I was still listening to my old Quads, which required me to ignore a few shortcomings to get the midrange. To me, that's where it has to be right-- if it isn't transparent, grainless and dimensional, the rest is irrelevant. But, that also takes us into the quality of the recordings- and my preference is for simpler, less "produced" stuff. 

I think if you listen to any system long enough, you will hear the "man behind the curtain." It is at best an illusion. 

And, though I don't think my system is fatiguing, I don't have the stamina I once did for all day listening sessions. Those used to be common when I was much younger. 

 I think making music is actually even more engaging, though I don't really have the chops I did when I was a kid. In NY, we would occasionally have visitors who were professionals, and they'd do their thing, informally. That was great fun and in some ways, much more engaging than hi-fi. 

Interesting question. Sorry I did not have time to make this shorter. 

Such a cool freakin' thread.  That's pretty much all I wanted to say, but I guess I have few tiny thoughts to add:

"Effortlessness."  That damn word.  I use it to mean the system is not pushing the sound to me, it's just letting it through.  I don't use that term to describe my listening experience, as in "listening for 72 straight hours was such an effortlessness experience."  So, the music itself could reflect lots of effort, but it's effortlessly communicated by your system.  Yeah, I'll take that.  But, honestly, maybe I'm using the term incorrectly.

To OP's point: I don't want my live music to be effortless.  I wanna admire the effort.  Not like watching Neil Young play an electric guitar; that's more than effort -- it's combat.  More like the focus, study, practice, and delivery that goes into a professional musical event, like Reckoning's Bird Song.

But the line of the thread is "It's something that is unamplified, has the highest quality acoustic instruments and most talented & trained singers - AKA the scenario where the matter of fidelity arises."  IOW, 75% of us are thinking of live music as the stuff we hear live -- via a PA system.  And, ya know, think about that.

I think it really depends on the type of music being listened to. It is a very difficult to reproduce a full symphony orchestra with fully frequency extension & full dynamic volume.  Conversely,  A truly good system can sound much better than many of the amplified rock concerts I’ve heard in the past 10+ years that are amplified & use the line array speaker design to supposedly offer the same balance & sound level throughout the venue. Most of them sound very hard, bright, dynamic but fatiguing. There are many good speakers out there that have very tone & body but few can actually present the dynamics of live music w/ full frequency range & realistic volume levels. For myself, good horn speakers with good tube amplification can do it. 

Different styles of music and recordings, some of which we don’t want to listen to for 24 hours. Put on AC/DC Live and you’ll enjoy the album and be satisfied when it’s finished. My system gave me all the energy and volume I could have wanted at the time but it won’t have been what it truly sounded like there. However you play some delicate vocal with a couple of accompanying instruments and you might find it sounds very lifelike and isn’t fatiguing. I guess systems can do both depending on the music genre and recording. For my main type of music tastes I can listen to my system for hours on end without feeling fatigued or having a headache, but I couldn’t put AC/DC on repeat at the kind of volumes that music requires to come alive. So for me I think a system can do both, it just depends what you’re listening to at the time. Having said all this, I don’t believe any system will truly be like you’re there, I just think it sounds as close to that to people who have the experience.