Listening skills are IMHO developed when you have a 'reference' and a 'goal'. If you don't know what is possible you don't have a reference. If you don't have a goal you don't know exactly what to listen for.
I agree with T Bone (mostly), you don't go to a live event for anything but to enjoy the music. While what you hear there could be a 'reference' it could never be a 'goal' because you could never replicate it at home (or even come remotely close).
Although I must admit the other night I heard a professional guitarist audition 3 new guitars against her own in a recital hall. The differences were clear for any one to hear but with her developed listening skills she could articulate the subtle differences in a more meaningful way when talking to the guitar maker. I could hear them, and they made sense when she discussed them, but I could never have described them so well. But now, if I were in the market for a new guitar (not an audio replication of one) I would now have a better 'reference', be able to create a realistic 'goal', and end up with a guitar I could be happy with.
In another, but relevant aspect, earlier that night she was conducting a master class with some college classical guitar students. She was talking about their technique in creating different complex tones. It was Greek to us, and the students as well, until she broke her comments down into playing just a few short notes using the technique, then it rang clear as a bell. You couldn't miss it!
I think many folks approach listening to an audio system's performance from the same prospective that they listen to music, they are 'seeing the forest'. When listening for system evaluation you have to be able to walk into the forest and examine each tree and learn to distinguish the difference between the Doug firs and yellow pines. It is there to hear but you have to learn how to focus on particular aspects and ignore others. Sonically there is an awful lot going on at the same time........
For example, how could you ever fully appreciate when you have achieved good soundstaging without ever having heard what is really possible.
You must get out and hear other well set up systems. Once you hear that 'great system' you have your aural reference, now all you need is a couple of great sources and some specific goals, and a lot of patience. It also helps when you can get other experienced ears to help you through this process.
FWIW.