A slightly different perspective…
I’m not a classical musician, nor am I a very good reader, but I’ve been playing and performing music all of my life. What saves me is that I have a very good ear. I can hear what is happening with the music, even if I don’t have a keyboard in front of me. This allows me to learn songs by listening to them, often while driving to the gig where I will perform them that night.
Our band has a list of over 200 songs. I do not use any notes, and we do not use set lists, so I may be called to play any of those songs with no warning whatsoever. For me, this is not difficult. We also may change songs on the fly, subtly altering chords or sections depending on our mood. This is also not difficult because I’m always listening intently.
Now, if I had to read charts or sheet music, that would be VERY difficult for me. Thankfully, I’m not asked to do that very often. The interesting thing (to me, at least) is that I’ve learned to play many of these songs while performing them in front of an audience. There are various “tricks” I use to accomplish this, but essentially, I’m using my ear’s ability to identify intervals and chord changes on the fly. So if, for example, I’m playing an F chord, I can hear instantly that the next chord the band plays is a 5th above, which is a C. My reaction may be slightly delayed the first time around, but I’ll have that change memorized by the second time. Or, if it’s a more difficult and unpredictable song, maybe the third time.
I dated a classical pianist for a few years. She got very annoyed at me because she could be working on a piece for weeks and, during that time, I heard it enough to learn it in my head. She would struggle with a section and I would say, “it goes like this” without looking at her music. She could play very well if that music was in front of her, and she could memorize it over time, but she couldn’t learn it by just hearing it. If I asked her to play a simple children’s song like “Mary had a little lamb”, she would struggle to figure it out by ear. We had entirely different skill sets.
All of that said, classical music is much more complicated than the music I play, and my skills will not get me a gig with an orchestra any time soon. But I suspect that there are few classical musicians who can do what I do. There isn’t the same emphasis on ear training in classical music as there is with, say, jazz, or in my case, rock and roll. And I really don’t know how I do what I do, but it’s worked for me and given me many years of enjoyment as a performing musician.