Here's some more of what I was thinking. I'll go back and read what people posted.
More on that question
Doesn't it reeeeeally help you to understand and know what key you're in? It totally changes your perspective of the piece, I think. Yet, I've seen students that can play intermediate pieces fairly well, but have no idea of the key they're in. And if they don't know what key they're in, they obviously won't understand some obvious things about playing a key -- recognizing scale fragments, I IV V chords, etc.
Ditto that with even the concept of a scale. Decent performance, but the student doesn't even know what a scale is.
That's something that concerns me with the idea of breaking a piece up into sections and then learning to play each piece and putting those pieces back together as a whole. How should the student go about learning skills like reading the chords on a page? And being able to use those skills at sight? This isn't necessarily part of learning a piece by the "divide and conquer" method.
I suppose you could say the same thing about serial music. I might be able to play it well, but I don't have the skill of seeing a tone row at sight. Being able to do that would definitely help my ability to perform the piece and my efforts in learning the piece would be amplified. I can sit down and anlyze the tone row, but keeping that tone row in mind while performing my be quite a challenge. Not that I'm going to start learning to "read" tone rows on pieces any time soon.... but the idea can be applied to any concept in music -- reading chords, reading the solfege/step of the scale, reading chord progressions (being able to instantly recognize a II V I progression, for example), reading the form, etc.
Do you get the gist of this concern? Do you have any thoughts on this?
I suppose the solution is that you play pieces for the sake of playing pieces and for performances, and then you also practice these "reading" skills to enhance your performance and learning capabilities.