Very few people can remember āallā the pieces they played. Depending on how a piece is arranged, there are some pieces you can sit down and work out the sequence by ear if you have good ears. I came across a lead sheet version of āSilent Nightā with several chords including C, G & F. There is a lead sheet version of the Simon & Garfunkel āSound of Silenceā with just 4 chords. I showed a friend who plays guitar: Dm, C, F & Bb. The melody with 5 variations is easy to follow by ear.
IMO you can train a student to be a good memorizer or reader early. While traditional piano lessons focus on developing reading skills, Suzuki requires students to learn the Book1 pieces by imitation off the teacher and soundtracks on a CD before learning to read. A student can be conditioned to listen to sound sequences and remember them. Itās like somebody talking about an article in a newspaper. We remember the content based on what was said than having to re-read the page to get something out of it.
The last piece I worked on was a Bach Bourree with 24 bars on 1 page. Has some awkward fingerings. Otherwise repeating the sequences by muscle memory isnāt too bad. Muscle memory is unreliable and requires regular repetition. If you havenāt played a piece for a while, you need to relearn some of the notes. The rest would come back quickly.