This thread is taking two tangential paths; that of the perceptions of a listner, and that of the aspirations of a studio.
Taking the latter first, I observed to a mixing friend of mine when we were on a live job together (a folk festival) that I didn't want to be thanked for the sound (which they often do) and would much prefer to remain invisible and anonymous. He asked why and I replied that as far as I was concerned, we should be invisible in the process of people's enjoyment of the show; they should not even be aware that we exist. He agreed, but then went to point out that so many gigs like this endure bad sound that it can come as a bit of a surprise when they get good sound, and that it's okay to accept the credit.
In much the same way, when I undertake a recording project, I don't particularly want people to say "wow, that's great sound" when the artist plays the CD to someone else. I'd rather that they didn't even consider the recordng process when listening to it; that the CD would be so good that the means became invisible when they enjoyed the ends.
When listening to music, my reaction depends on context. When I've got the radio on in the car, I react to the emotional impact of the song, rather than any technical dimension. I don't even care about the lyrics (even though I spend a huge amount of effort working on my own lyrics) so long as the sound of the words and the way the consonants fit together line up with the general sound of the song.
On the other hand, when I am reviewing CDs, part of the review includes a technical assessment, so I pay attention to the process as well as the content. But even here, my reaction will vary. For example, sometimes I am doing something else, so I stick the CD and have it running while I'm otherwise engaged, and again it's the overall feel that grabs me first. But if I sit down and listen carefully, I notice the technical things first.
In my younger days, I didn't understand anything about musical quality, and I listened to and loved everything; whatever I could get my hands on. In those days, quality was invisible to me.
Over the years, and specially those spent heavily in music itself, my ears are a little more refined. Sometimes I play those songs I loved so much from the sixites, and most of them sound terrible, and my enjoyment is sadly diluted. When deliberately listening for pleasure (as opposed to for reviewing or as a peripheral to something else), I find I generally don't enjoy music as much if there are aspects of the recording that grate, even if I can appreciate the artistic endeavour behind it.