Great points! I've seen a couple of papers on CLA for music learning, but CLA is a subset of so-called "non-linear pedagogy", so maybe music education has its own "branch" of it, so to speak.
> I held the belief there was a "perfect way to play" the piano
Yes, CLA is actively debunking the myth of a "perfect technique" which is very popular in sports. Like a coach/teacher is one who knows the "perfect" way, and their job is to make students repeat an exercise over and over again, fixing deviations from "perfect" technique. This couldn't be more wrong according to CLA.
Already mentioned Bernstein introduced the concept of "repetition without repetition", which claims that repetition is important in learning but for a different reason. Each attempt of a movement will have slightly different "inputs" - constraints – and thus can't have a single "perfect" technique that will work for all variations of inputs. Each repetition will be slightly different (hence "without repetition"), and the goal of the proper learning process is to give the body enough "input data" to _discover_ the proper movement solution.
It's important to note that "constraints" is a wide term here, and there are few classes of constraints. Task and goal given to the student are constraints, so the size of the hand or level of fatigue. Even environment temperature, mental state, and light conditions are constraints.
Another important concept in CLA is action-perception coupling rooted in James Gibson's theory of perception. This one was mindblowing to me when I first read it. In essence, the brain perceives the world not as a set of geometric objects but as "actionable" items. What you can do directly influences how you see the world. That has direct implications for learning as well – mastering any skill (including playing a musical instrument) is coupled with perception, as your body has to react to how it sees/hears the result of its own movements.
But the core of CLA as an educational philosophy lays in acknowledging that the actual learning still has to happen inside your nervous system. You can't really "teach" a skill, only facilitate a discovery inside the student's body.
It's really fascinating how it all works in practice. One related concept in motor skill acquisition science is the Method of Error Amplification (MAE). Let's say, golf players make a fundamental error of not shifting weight onto the back foot after swinging. Instead of giving them verbal instruction "Shift weight to the back foot", coach might do the opposite – ask them to move weight to the *front foot*. This will increase the error, which will amplify the signal in the nervous system and the body will react to it as it now feels "more wrong" by itself. It's not super clear to which types of errors MAE is applicable, but the research on MAE is fascinating.