I agree with you that the analogy with music and programming is not exact. HOWEVER...
I think that the music equivalent of programming would be something like song writing or composing. With playing a song, your are really just following the instructions that somebody else gave you, like following a recipe in a cook book.
I think that's a bit of a misunderstanding of how one gets to the "top tier" of musicians, and for that matter, how one becomes a great chef.
It what you say were true, no violinist would ever bother recording another version of some piece of music. In fact, nobody would ever bother even going to see a concert of a standard piece, since there would be nothing new -- it would just be the same "script" or "recipe," and most well-known pieces already have arguably a number of "perfect" recordings (at least in terms of "playing all the notes in the right rhythm and in tune" or whatever your standard is).
No pop star would ever bother recording a cover of an older song. After all, a great singer already did it.
But of course that isn't true. Composers don't generally write every single detail of interpretation in a score, just like there's a lot of "unwritten knowledge" in most recipes about how to actually produce good results. Beyond that, music is a process that happens in real-time. A skilled performer will be sensitive to everything from how their instrument sounds that day to the quality of acoustics in the playing environment to the fact that today they just happened to play the high note in that first theme a little stronger, and maybe they'll bring that note out again a little later because it creates a cool connection (which listeners may not consciously be aware of, but it suddenly brings out an emotion or creates a feeling of continuity which changes the piece).
Performance is an artform at the highest levels. You may not be interested in such nuances, and that's fine. But people who spend hours and hours every day of their lives practicing instruments aren't just "learning notes." They are developing techniques, learning ways to produce better interpretations of music (beyond the basic blueprint in the score), gaining a facility to make real-time adjustments that will create a better experience for listeners at a live event, etc. Similarly, a skilled chef may follow the same instructions you do from a cookbook, but the result in quality may be vastly different. The execution often makes the difference between mediocre and truly great.
I've had people tell me that a particular piece of music was worthless, even when played by top performers who can do flawless execution of the notes. I've then played them a recording of the exact same piece (with all the same notes, played from the same score) played by another performer -- and I've had people say they suddenly thought the piece was amazing... they heard things they never did before, or it had a kind of "energy" that made it enjoyable or whatever.
Anyhow -- this isn't just about music. It's recognizing the value of performance in all walks of life. It's also about recognizing how great artists, whether they generate a product or whether they perform on a stage, are able to tap into dynamic and creative processes to produce effects that are much better than others. You may have been given the greatest set of Powerpoint slides in the world, and you may basically follow a script for a presentation -- but there can still be a huge difference between a completely engaging live presentation and a crappy one that "just follows the instructions that somebody else gave you."
I know you probably didn't mean to denigrate performers, but I think we often tend to think of what's written down as the "primary stuff," no matter what line of work you're in. But there is a lot of knowledge and skill that's passed down orally and learned verbally or through tactile/kinesthetic engagement which makes the difference between following a recipe and cooking like a chef.
And, in that sense, I think there are some interesting analogues between music performance and programming -- because a lot of what makes great programmers great is their ability to see patterns and connections that can't just be expressed directly in some book on programming techniques or syntax or algorithms. That's the kind of knowledge that often comes from a combination of talent and experience -- the kind of experience you get by spending hours each day tackling various problems in slightly different ways over and over.