If classical composers ever started notating like that, I would stop playing classical music.
I'm curious why? I'm not advocating for getting rid of the staves and the notes, just addiing additional notation above the staves the same way pop music puts guitar chord symbols. Classical harmony can move very quickly (several chords per bar) so maybe it would be unwieldy in practice but I don't why it would be so very dreadful. What about it rubs you the wrong way?
Maybe what rubs people the wrong way (and this is only a guess) is the idea of approaching a piece of classical music as you would a piece of pop music. In jazz, for example, the performer and composer are one. Give a talented jazz pianist a fake book, and he's good to go. It's like giving a painter a canvas with only the broad outlines of scene, and then saying, "OK, make it your own." That is why jazz musicians are so admired, and even envied by classical musicians. Improvisation is truly an amazing talent, and few in the classical word can pull it off, without sounding - well, too "classical".
But in classical music, there is no broad outline on a relatively empty canvas. The picture is already complete. Every stroke, every color is already there, and it's the artist's job not to add or subtract, but to restore it and make it live again. So I think the whole idea of notating chord progressions suggests that you may still be thinking in terms of a framework, within which you can "play" (as opposed to play). But as I said earlier, in classical music, every single note counts, and every note must be played. There is no note that is simply extraneous, unless you are bold enough to second-guess Chopin.
Maybe you should ditch Chopin for a while and try some Bach. Bach's music, (especially his fugues, which are very linear in nature), might move you away from your more "vertical", chordal way of thinking. I think you'd find your chord notations meaningless. You would begin to focus on the melodic and thematic aspects of music, rather than the harmonic. I came to love Bach at a young age by listening to one of his greatest organ works, the "Passacaglia and Fugue in C Minor". Beginning with the Passacaglia's foreboding introduction of the theme (on the pedal board), Bach takes you on an amazing journey of endless variations, with "the theme" exiting and re-emerging, but omnipresent. I doubt you'll be thinking much about chord progressions. But more like, "So where's Waldo now?"