I've never, while pursuing my development as a pianist, given thought to hand position in its rudimentary definition.
I'm interested if you could expound some more, in your third point especially,
Occasionally, I have to remind younger students to keep their thumbs on the keyboard
I think. A "natural" hand position is truly the way our hand exists when at our side while standing or casually walking. If I have a student with unusual issues regarding hand position, I will have them stand up with their arms at their side, then tell them to sit down without bothering their arms or hands, and then I simply place their hand on the keys.
Did I read this wrong? Keep their thumbs on the keyboard?
No, you read correctly! Many of my youngest students like to play with their thumbs quite far away from the keyboard, which tends to compromise the natural shape of the hand.
3. Formulaic - I believe that, while there are physical characteristics of a natural, relaxed hand position, a truly natural hand position as it relates to the piano is a matter of a calm, trusting psyche and a kinesthetic understanding/relationship with (musical) note-groupings - and that I mean very literally. Groups of notes, not just one, in relation to the whole hand.
This seems like three ideas to me.One is whether to prescribe a hand shape at all. I tend to think that may be a good idea. I'm not sure a beginner always lucks into a usable one. The next is whether the commonly prescribed "grip the ball" is overly tense and rigid and needs to be replaced with a more modern understanding. This sounds logical but I'd defer to your experience on that one.The third is that all students have the same learning style, and your focus on the psyche, with the implications of an "inner tennis" oriented approach, will work for everybody. I would disagree with this. I think learning styles are almost hard wired, and a one size fits all approach, even as general as this one, is doomed to failure for the students that don't match.
So are you basically saying that some individuals benefit from and find the most natural-for-them technique with specific instruction on how to hold their hand on the keys?
Yes, precisely.
Contrary to most -- if not all posters here, I start teaching the right hand position right from Day 1, regardless of the student's age
I don't like to talk about curled fingers. I find it to be confusing for students and parents alike, and can lead to a lot of tension and rigidity. From the first lesson, I talk about joint stability, and I don't stop talking about it until it's firmly ingrained in the student. Here's a video I made on the topic.
To take one point, for example, a "raised" bridge at the first joint is not actually, truly raised. It's not lifted, and the height at which we sit on the bench (as well as other factors) comes into play on this, too, even just in the way our hand appears to be on the keys. But, when the first joint is supportive so that the fingers can hang, it is actually a result of the hand being in a natural, resting position (which is what I actually see in your own hand when you talk about it being "raised"). It is possible for it to be thought of as "raised" though, as though we must somehow cause it to go there, and suddenly, one wrong step along those lines, and we have more challenges to deal with. Not to mention that it's eventually important to not think we must keep our hands in that precise position at all times, and it's very easy to fall into thinking that we should! I realize that part of the problem is simply in trying to verbalize concepts that can't be perfectly verbalized, but that's part of the reason I resist verbalizing them!