Yes it can and it has been - it's called digital audio.
But people tend to prefer the rock in the groove.
Mysteries of the universe....
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Different cartridges/tonearms will produce different signal by reading the same microgroove. Different CD players will produce different signal by reading the same digitally stored information. Some people pay a lot of money hoping that the resulting sound will be to their liking.
Mysterious...
But it isn't. Well, I agree about the 'liking' bit is as that's psychological and a very complex system with lots of variables and unknowns; but the reasons why cd players and cartridges don't sound alike are completely quantifiable. I suppose if you get down to one type of capacitor sounding different to another, maybe that is not known why. Or maybe it is? I don't know about that.
Well look at reel to reel. It is just metal magnetized to varying degrees. Vinyl is just a continuous groove cut into plastic. A CD is just pits and lands, a music file just noughts and ones. Whatever the medium it is just a simple instruction to vary voltage with time. The difficulties come when you transfer the signal it carries from point a to point b in order to listen to it, lots of nasties hitch a ride along the way and dealing with them all effectively is non-trivial, as they say.
To me, a simple signal is text stored on either magnetic, or optical medium. If I type a few paragraphs, and then store them on USB drive, then take that USB to a friend and he plugs it into his computer and loads it, we'd expect all the words I typed to appear intact, in the same order I typed them. The reader should not remove any characters, nor add any characters, nor jumble any characters.
That's simplicity, the way I see it. A simple signal gets stored and then gets simply restored with 100% accuracy. It never fails (unless the medium gets corrupted along the way, of course).
How come we cannot achieve the same accuracy with musical signal? If, as you say, it is equally brain dead easy to capture and store sound, why is it so devilishly hard to restore it to its original shape without adding or subtracting or jumbling things along the way?
Temporal reasons which the example of text does not require for fidelity.