Playing pieces from sheet music has nothing to do with "exact" replication. It has to do with understanding a work and faithfully interpreting it in your own style. New interpretations of the Hammerklavier and the Paganini caprices come out rather frequently.
Once a piece gets to a certain scale, it becomes incredibly hard to do that without musical notation. Picking up each note by listening to the piece over and over just becomes intractable.
It also has nothing to do with how old a piece is - modern composers also use written notation as the primary communication medium of their musical intent (new music often comes with a MIDI mockup which is a poor replacement for a past recording).
Finally, I would suggest that the point of music education is to give you the tools to express your musical ideas. Some people want to play Liszt and Paganini - those pieces are really fun.
I completely disagree. Firstly, the entire value system of believing that one ought to play the Hammerklavier sonata exactly as played before is questionable.
I was trained to read music (and very little ear training) and honestly made to feel pretty terrible as a piano student due to my inability to do so without fidgeting and being a general 'problem' student. Funnily enough, for the ear training we were made to do, I was even 'ranked' bottom of the barrel. My brother was ranked high in all the categories
Except... here's the thing. Throughout my experience, I have been able to basically play anything by ear. In fact I can pretty much hear a song and play it on the piano (of course the classical training helps in terms of technique). I also produce tunes on the fly, and generally am entertaining. My brother (by his own admission) does not. He is a very good player for sure, but he has no interest in music. Yet, our 'classical' musical education ranked him higher. Thus, I really question the entire value system of forcing kids to 'read' music and only judging them on their ability to replicate, which seems to me to be the bulk of music education.
We must ask ourselves... what is the goal of musical education? To produce automatons that can replicate any musical piece written or to create a musician?