I am not commenting on the quality of the sound so much as the liveness of it. I have heard some horrible live amplified concerts as well.I am not sure. Acoustics and sound system performance 'at your seat' can be patchy indeed. I went to some Flamenco last weekend, at a decent theatre, and we were a bit close to the left side channel speaker column. It was thus a bit too loud / shrieking, and certainly not without distortion. This is live music performance I am referring to, not studio conditions.
So there has been plenty of live performances I have heard with some elements of distortion. Female voice seems very hard to amplify really well for example.
One thing that IS apparent on live music is often the huge dynamics, there is a lot of energy and power reserves in the drums and bass for example. That is difficult to portray in home sized speakers in general. But linearity, lack of distortion, smoothness of tone, that can IMO be better in a good domestic system. So within it's 'envelope' I do think a good domestic system has strong points even compared to a lot of (amplified) live music.
Btw, I heard a fantastic Flamenco concert back in 2017 in Granada...now that was some powerful stuff!