I don't obsess or even think about a recording sounding like an actual live performance. I only think about how great a recording might sound or possibly not so good if it is produced poorly or is just a lousy pressing job.
I will say that some stripped down acoustic recordings could sound more like a live performance than more complex recordings.
I usually thoroughly enjoy what I am listening to because I am very happy with the sound of my system(s) and the music that I choose to listen to.