If improvisation can not be taken as the norm, then let's at least take transposing on the fly. I find it incredible that people should play something by chopin in c# minor but would not be able to readily transpose that idea into another minor key on the fly. It's almost like being able to recite a work by James Joyce by heart, but not being able to say anything sensible in English.
Everyone always seems to associate improvisation with pastiches and potpourris. For me, it's its own thing. We can incorporate musical vocabulary from a wide variety of musical cultures spanning hundreds of years and thousands of miles.... but ultimately, it's really about having your own style.
I can see your point, but it's craft rather than art.
Remember, please, that I said what I said in the context of SIGHT-READING, which is also a craft. I find it UNACCEPTABLE that people should abuse works of art more than one day to just learn the notes. In that sense, sight-reading is their "real" level. Improvising (in the sense of arranging existing melodies on the fly, not in the high spiritual sense awesom_o has in mind) and transposing are skills of the same kind.P.S.: Exploring sound takes a lifetime.
Sightreading is a necessary craft though- to meet basic requirements of being a classical pianist. Transposition skills are a hell of a bonus to have, but they are not an inherent necessity for someone who wants to make artistically rewarding results.
In the light of the OP, how can one sightread effectively what one does not understand or recognize as familiar vocabulary/idioms? I would rather first introduce the vocabulary to the student, and then have it recognized through sightreading. Give them an alberti-bass type of thing for the left hand to play with in all keys and you know yourself how many Classical works of art they'll be able to do at sight.
To what end other than itself? Where does your own compositional style show up in that Chopin nocturne?
This example makes sense. Of course, it's practically useful to be able to play it in all circumstances- ready for any that will arise in music. But to transpose a whole nocturne from memory (rather than a small unit that would be expected to widely recur in repertoire)?
Maybe I didn't express my thoughts clearly enough. I did not mean transpose the whole work into another key; that would be something like a circus act. Just take a motive + harmony and play with it in just about any key. This seems quite natural to me. Most importantly: one should have enough hand memory to be able to take the required new positions on the fly, which has a lot to do with sightreading.
If you already appreciate it in one key, you don't need to be able to transpose it to bring out the interest.
When you practise some of Chopin's passages in symmetrical inversion, you may get quotes of works by Beethoven.
Given Chopin's aversion to Beethoven, that'sa the equivalent of playing a Death Metal band backwards and getting the Hallelujah Chorus.
Chopin's Favorite Beethoven