There is more than one way to appreciate music. There is somewhat different cognitive equipment developed through the process of becoming a composer, arranger or performer.
A high level audio engineer also has specialized cognitive equipment. Among the audio engineers I've worked with there are skills specific to live sound that are distinct from studio tracking, mixing or mastering. Audiophile listeners also have specialized cognitive equipment. They're all good, but there is a tendency for people to underestimate skills they do not possess.
A classical pianist can listen to a performance of Vladimir Horrowitz on a mediocre stereo and really enjoy it. They know in minute detail what a really good concert grand piano, tuned and voiced by a world class technician, sounds like.They also have the score stored (and can see it), along with a bunch of other information on harmony, articulation, balance, phrasing, dynamics, fingering etc. They also know that even a single change of fingering can shift the feel of a phrase. They may have also played that particular piece thousands, or even tens of thousands, of times. (Daniel Beremboim, admits that in his practicing he spends more than 90% of his time practicing nuances that less than one percent of his concert audience can even hear.)
In a similar way a high level jazz pianist will have listened to the music they consider formative with an intensity that verges on vengeance. They'll put the recording on a slow-downer, slow it down to 20%, then save it in a file, then slow down that file to 20%. From there they will filter out all the other frequencies they aren't interested in and focus on and transcribe the finest, quietest nuances that you cannot possibly hear in the native unaltered recording (because they get covered up by the ensemble). They'll internalize that until it becomes fundamental to the way they practice.
Turns out human brains can use little bits of cognitive equipment
from a wide array of skill sets to modify perception. In the case of
music, a listener's brain can zoom in or even clean up the signal so that what they hear is better than the original.
Please don't get caught up in the equivalence of chest pounding routines. Your kids could distinguish between songs in major and minor keys before the age of two. That's cool. But don't let it blind you to all the other nuances in the music you're listening to.