alt Hacker NewsMusic is an interesting case. You can't slow down the consumption of music (you have to let it play at the speed the performer intended), but you can dial up the attention you give it. Listening with headphones, eyes closed, and phone+doorbell etc. switched off would be close to max. Sitting at a live concert (I am thinking classical) is up there too, because you've given yourself permission to not think of/work on anything else in that time. For music, we can say that the default settings are too LOW.
And similar to the point OP made, you get more out of it when you attend more closely. And similarly, most music does not withstand this level of scrutiny.
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You certainly do not need to play music at the speed the performer intended! There are whole genres (and subgenres) based on this. :) Personally, I have found that slowing a familiar piece down by ~5% tricks my brain into perceiving it as novel again, which helps me attend to it more closely and appreciate it more.
I've taken the time to rebuild a large music collection locally. I've adopted every CD collection my friends and family have set aside to rust. It's immensely satisfying to scroll a gigantic list of 40,000 tracks and just pick whatever feels good, knowing I'm not contributing to a profile on my listening habits and that the file will instantly play flawlessly.
I have some excellent garage band CDs that probably have two or three copies still in the wild at most. Unfortunately sometimes the 25 year old burned CDs are missing the TOC data, but even the recovery process is satisfying.
(Same with the DVD collections.)