Early learning should be focused on musicality and improvisation, not refined performance technique. Historically, even music in the so-called 'classical' tradition was mostly improvised. It's only in the late 19th century or so that technically virtuosic-performance playing of old repertoire became the only known standard of quality; but what those pieces of music were intended for originally was something quite different.
There'a been a comparatively recent revival in classical improvisation largely focusing on the partimenti and solfeggi tradition, that arguably points to a better way of teaching even 'ordinary' music performance as well. After all, even a "proper", non-robotic performance of a piece cannot be achieved without some appreciation for the musicality of "how the piece goes".
I agree. The idea of perfectly reproducing a performance note for note may have been impressive before recorded music, but now it's the boring default. When people talk about a "song" they really mean a particular recording of a single performance played metronomically over a grid.
People are starved for the human touch in music that comes for free with any live performance. In most of the US there is so much focus on mega pop stars executing perfectly planned shows with exorbitant ticket prices that there is little exposure to real improvisation. My hope is that people jamming together for fun can regain its place as a cultural staple in this century, but it seems like the barriers are higher than ever.
This also tends to be my view because improvisation is what I enjoy doing musically the most, but my daughter (12 yo) takes piano lessons which are quite typical in their structure (Conservatory) and has no interest in improvisation, and in fact, has resisted my attempts to get her to try it. She's obsessed with classical music and practices all the time with no prompting (and is now able to play quite beautifully), so of course, I haven't continued trying to change what she's doing.
Perhaps what are needed are methods to determine the approach that will work best with a given child.
I disagree with you, and I think that if your daughter has found something she likes doing with the instrument, you should encourage that, even if it's not what you wanted or expected.
As a child who loved classical music, I hated getting comments from my relatives that I should play them some rock or jazz. I just wanted to do my own thing. Honestly, it's also a very different style of playing - I later learned some jazz piano (to appease them) and it's less demanding on your fine motor control ("tone color") and more about playing precisely on beat, which I found a lot less fun.
I think you misread the parent post. They said that they stopped trying to encourage their daughter to improvise, because she took naturally to classical music and doesn't seem to care about improvisation.
Perhaps it's because it's how I taught myself, but I am in the camp that chords should be taught first (guitar or piano).
Notes, reading sheet music can come much later (if at all).
Two or three chords on either the guitar or piano is an easy start and will open up a world of songs for the learner.
I watched my daughters take lessons and tediously work through reading sheet music, learning scales... I thought it was no wonder they hated it, and no longer play an instrument.
I once attended a workshop by a guy who had been a salesperson for Piano I, Piano II etc books. He noted that sales of those fell off geometrically for each successive book. So he basically advocated/hawked an improv and "fakebook first" approach, as a means to make enjoyment [potentially] primary.
I had an interesting night some years ago interacting with a Google piano ML available online. It would broadly mirror your input is a sort of call and response way. Even with only a qwerty keyboard (i.e. home row) and really elementary melody/stacatto it was remarkably pleasing. Relatedly, This could be one reason I anticipate great potential with GPT-like tutors.
There'a been a comparatively recent revival in classical improvisation largely focusing on the partimenti and solfeggi tradition, that arguably points to a better way of teaching even 'ordinary' music performance as well. After all, even a "proper", non-robotic performance of a piece cannot be achieved without some appreciation for the musicality of "how the piece goes".