Yep the music does not change and we all hear live recordings as live and real (no matter what coloration the room throws at it).
It becomes funny when you are in the audience and record the sound where one stands and listens to it.
Now... do that at 2 different locations and compare those recordings... they will sound very different and very different from how the live music was perceived.
Our brain calibrates itself constantly for sounds around us and as long as one isn't autistic filters out a lot of irrelevant crap. This is particularly true when we can use the eyes (and body) as input as well.
It becomes a different thing when listening to headphones. Simply because our brain is missing cues (no crossfeed and artificial hall/echo) as the sounds come from the sides.
Our ears are not really designed for this.
Also sounds coming from 'in front of us' (speakers/live sound) is reaches us in a certain way and sight helps (unless one is visually impaired then things change).
We don't see sound sources from the side. Brain only 'knows' it doesn't come from in front of us.
Yet this is what we do with headphones. Sure we can use crossfeed or other trickery and modify the FR of the recording to suit our HRTF but still the coupling between 2 small speakers a few cm away in a small (closed) 'chamber' differs from actual point sources far away and in front of us.
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Add to that the rather 'wonky' FR response (but usually good phase response) differs from what speakers on a distance do (other type of FR modifications, echo's, hall, phase and nulls). Not to mention seal and positioning on the head, lack of tactile feel which not everyone will 'hear' the same way.
And agreed, with speakers you don't compensate for HRTF, the brain does that for you and is remarkably good at that.
Speakers and headphones, however, with sounds coming from very different directions have different HRTF so it makes sense to compensate the difference between hearing sounds from the front and side of us if the goal is to get 'realistic' sound.
Recordings are means to be heard from 2 speakers in front of us ... unless they have been recorded binaural.
It is well known that ears and ear canals differ individually (and differ from fixtures as well but is another matter). For sounds coming from in front of us this does not really matter as the brain takes care of it.
But sounds coming from close proximity from the sides where for instance the pinna is also deformed (when touching the baffle, bypassed partly or completely) the ears are not 'calibrated' by the brain and hear it differently for coupling reasons. Especially above a few kHz the differences can be dramatically different from sounds coming from the front of us.