It's very helpful for me to get the perspective of experienced teachers here, but I'm finding I still have a lot of questions about phrasing.
Let's take a student who is only interested in popular music, not classical, and who might even be learning to play by ear. Surely one of the very first things he/she would learn is how to play a melody in the right hand that had a musical, "vocal" sound to it. Granted you couldn't do this the first week, or maybe even the first year you started to play, but how long could it take if you made that your goal? If you have a good ear, it could happen very fast.
Contrast this with classical music, where for the first x years you learn how to read the notes on the page, and various technical issues. If your teacher is chopping up your trianing into little chunks, focusing on one specific problem at a time, at what point do you learn how to make a piece sound like music?
I'm not saying that technical matters aren't essential, but shouldn't there be time somewhere for another approach? Call it ear training or improvisation or whatever, but I have a feeling there are an awful lot of classical students who envy their peers who can play popular songs off the top of their head.
Let's take a typical easy Chopin waltz, mazurka or prelude. Basically you have a melody in the right hand and a fairly basic, oom pah pah type accompaniment in the left. Is this really that different in form from a popular song? Certainly waltzes and mazurkas were dance music in their day. Could a student learn to play the accompaniment in a rhythm that can be danced to, while the melody sounds like something that could be sung?
Now I realize that Chopin in particular is more subtle than that -- just when you think he's waltzing along he throws in a section that makes you stop and think. And there are always little technical trouble spots that have to be fixed. He can't actually be played like popular music. But could he maybe be approached from that direction?
An approach that tells the student "your goal is to make the music
sound good -- everything else is just a means to that end."
For me, as I approach my twilight years

I find more and more that that's all I really care about. I'd rather take the easiest piece out of my piano bench and make it sound beautiful than spend a year struggling with some virtuoso etude and never get to the point where I can play it so it's actually worth listening to.