High barrier to entry skills like playing a piano don't conduct themselves well to random unguided exploration. And in music there is often a warning that doing so may ultimately restrict your potential in the field.

Internal martial arts has the same warning. Across pretty much all disciplines in the field, the message is that you can only learn these skills kinesthetically. Not talking, not seeing, but feeling instructor corrections with your own body.

Im not sure why that’s a common sentiment but I disagree that unguided exploration in music is not conducive to productive learning. Or maybe you’re just talking specifically about classical piano which I guess sure that makes sense but the piano is way more versatile than that and I encourage anybody to pick up a keyboard and just explore. You’ll be shocked how much you can accomplish and theory is always there to learn later once it becomes relevant to you.

I think you hit a interesting point. If you define a very specific set of criteria to judge skills by, e.g. "classical piano", then unguided exploration might be a worse starting point than no exploration.

But, if we accept a less restrictive/strict outcome, then unguided exploration is very likely a net positive. I think many well known "unorthodox" musicians did this, and also attributed it to exactly that. Though I cannot recall specific examples. So take it with a grain of salt. I'll look up who I suspect.

Edit: Searching for examples of largely self taught musicians, there are lots of examples. What this implies, probably varies wildly. So feel free to correct the examples I encountered: Chopin, Hendrix, Schubert, Uematsu, Bowie.

My problem was with representing exploration as an unqualified boon. It's not unqualified.

Um... I don't know why I am this way but I have uh... talent in both of these areas and I certainly did seek out training but... this reads to me like someone who could enjoy being an amateur. If we are talking about "skill" I would stay away from the music industry and getting into any fights. Martial arts can be a wonderful activity regardless of their actual impact on self-defense (and drilling combatives certainly can help). Likewise, music can be enjoyed by someone or even an audience regardless of skill level. But again, if we are talking about skill... I'm talking about kicking a* and getting paid and I figured out a lot of that from random unguided exploration. Whether in jazz or combat, everyone has a plan until they get punched in the face. Learn the few rules and break them. Your opponent will.

But the reason they are a student is because they can't play the music. Showing them the notations and demonstrating how to play it are steps towards them playing it themselves.

Not necessarily. Especially the notations are certainly not a necessary step towards the student playing.

Playing for them, sure. But you can play once and invite them to play. Not keeping showing until you think they learned.

Sure, you can have them learn by ear or learn by sheet, both possible. According to the analogy you can't do engage without doing either show or tell. Which one doesn't matter.