When I first got into this hobby, I definitely focused more on the technical aspects of songs. Now, the only time I listen critically is if there's a component change. Not to say I don't like listening critically to spectacular recordings, of course I do as do most of us.
You know you've hit the sweet spot with your system when you just listen to the music. That said, I still like to find the best recorded versions of what I like to listen to but won't lose sleep if I can't since it all sounds very good anyway.