Going off a very similar question, "piano notation implies that the upper clef is the part played by the right hand, while the lower clef is the part played by the left hand." Is there some technique that would be missed if one hand played d# and e over for the top and bottom of the grand staff?
From Bastien Piano For Adults Book 1, the middle of the Für Elise piece does something strange. The bass clef switches to treble, then the notes get relatively high (normally). See the beginning of the third line:
So now both lines of the staff are treble clef. The same two notes are played, but the piece makes it seem like both hands are suppose to switch off playing these same two notes: d# and e (upper treble), same d# and e (lower treble), repeat. I realize that most of the songs in this book are to learn certain music theory (rather than the piece alone), but do the Bastiens intend students to have both hands switch on and off? Or is Mr. Miyagi making waxing...tedious?