Two anectodes, one historic, one personal.
Historic. There is a famous letter of Mozart to his father, where he tells him about how a piano concerto (?) was received and how he felt about it. And as I remember it, Mozart says that he was quite happy with the concerto because "normal" people liked it, and expert musicians found intresting/intriguing/innovative things in it and hence liked it.
Personal. An undisclosed number of years ago 🙂, I hosted for a few days in my apt a friend of a friend who now is a famous conductor and back then was a student seeking admittance at a prestigious school in the US. We talked a lot about music, we played Schubert f-minor Fantasia together, he showed me some rudiments of conducting, it was three exhilarating days (for me at least 🙂). And towards the end, he was playing Elektra on my piano, showing me the daring harmonies used by Strauss etc, and then at some point he like stopped with a sigh and said---I'm kinda envious of you, who can just listen and enjoy instead of working all the details of a score.
What I'm trying to say is that "understanding" is a big word. Take the "risanato" slow movement from the a minor late beethoven quartet. What does it take to understand it? Do you need to understand/know that it is a hymn? do you have to catch its mystic character? Do you have to understand the gratitude for healing that permeates it? do you need to understand the ancient use of modality? do you need to grasp the subtle bits of the harmonic composition? the interplay between the four instruments? etc etc. It's a big term and it's hard to define it, to justify leaving something out of it. As it happens, some people will have the technical ability to "understand" more elements than others do. Some people will have a more basic enjoyment. Sometimes the former might encroach into the latter as my conductor friend implied.
I find it very interesting what was said in this thread: different audiences at different times will "understand" (or: will have the tools to understand) music differently than us. Maybe chamber music in the classical period was understood more than the generic audience of a classic concert does today. I doubt many in a concert hall today do know/understand the forma sonata, or the intricacies of counterpoint, while in the 1700s you could generally expect a higher level of sophistication from most audiences. So a lot of what we mean by "understanding" will depend by the "vocabulary" so to speak that one possesses. One learns about Galant schemata, and recognizes them and learns how to use them, and it's a bit like learning new words in a language, allowing you to understand or better undertsand what's said, and say things yourself, too.
Classical music is I think one of the most amazingly intricate forms of art that we humans have been able to generate. But music (some of it at least) has also this amazing property, that one could now nothing about theory, and still, like I was at age eight many years ago, be moved and engrossed and hooked by listening to a counterpoint of the art of the fugue. It's elusive, i think, to try and figure out what was there to capture your heart so fully. Maybe you learn how to play, you learn harmony, you learn counterpoint, you learn how to write a fugue, and yet you're peeling layer after layer of an onion, and in the end there's nothing left and what really captivated you remains ineffable. So you can understand the technique, you can marvel at the abilities of Bach, you can get a glimpse of why a certain solution was chosen and not another, but what links your heart to that piece, that so many times (most times? always?) remains not understood, and it's a big part of the beauty of music.