Today's lesson on the "Moonlight" with my computer-animator student revealed an important aspect of the perniciously invasive basis of traditional piano pedagogy.
After many hours delving into the mysteries of this great work I had him select a measure in which there seemed to be notable difficulty. He chose a measure of arpeggiation near the end of the first movement. As we worked I realized why so many serious piano students get sick of the great repertoire.
At the first lesson on a piece we are given fingerings. I maintain that the hand is the instrument, even more, perhaps, than the actual piano. Fingering is, then, the ultimate art of playing the instrument. I never write in a fingering unless I find that it reveals some cryptic element in the line that habit is likely to obscure every time I refresh my acquaintance with the piece. I can think of particular measures in Beethoven and Brahms that fit that bill.
Your hand is your very own and must freely reflect the action of your inner ear. No one else's, thank you very much.