I often wonder the same thing. I don't know the best thing to do.My students, beginner and intermediate levels, mostly learn a new piece every week. Now, at this rate, there is no time for them to develop perfection with these pieces. Therefore, I separate out pieces that they will work on more and develop to a presentable (not perfect, of course) performance level. For each of my students, their development of a piece is unique. By learning a lot of pieces, they experience far more reading, style, techniques, etc. Most students, if they sit an exam, will have played through virtually the entire syllabus for that level - enough to experience that music. Each piece they work on, I determine if the focus for that student and that piece is understanding harmonic theory, learning a technique, developing dynamics and phrasing, etc. In nearly every case, the students learn not only the focus but also have the piece at a passable level within a week or 2. They get used to this expectation. Sometimes we revisit the piece for an extra week, looking at another concept (or occassionally to actually achieve the first goal if they haven't practiced properly or have found it more difficult than expected), sometimes we come back to the piece after a few weeks to develop it at another level. Sometimes I wonder if I expect too much, give too much work - but most seem to keep up and I try to respond to where the student is at. I try to push them a little further every week from where they were the week prior, but do this by giving them opportunity to learn something entirely new. The goal and the standard is different for each student. Sometimes I wonder if I am not giving them the expectation or opportunity to develop pieces or to face new learning with already familiar material - e.g. learning a technique where they can focus on the movement rather than the extra demands of the notation. But, without the benefit of an outside assessment or comparison, I do think my students generally handle this well. The one area that commonly seems to be overlooked is dynamic variation - but they are able to correct this when going through the piece again during the lesson.I don't know if I am doing the right thing - I know each piece could be learnt more, but my students are mostly excellent readers (those who are not have a very sound theory knowledge, because I teach them how to understand / learn / memorise the music based on its structure - this is where the non-readers have an advantage over the fluent readers in my teaching approach; but the readers get more technical instruction). I think it is important to experience a lot of music - for musical development rather than the learning of a handful of pieces. Still, I hope I am not denying them something important - and I am keen to be told if I am.Sorry this is so long - it's just a question I have on my mind nearly every day.
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.
..... with classical music, .. 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 training 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'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.