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You ended up listening to Schoenberg at his best, and Sequenza is also a pretty good piece. As a composer and pianist/harpsichordist, my theory on this is that at some point, modern classical music became postmodern in terms of rejecting the concept of objectivity and beauty in the experience of music. That allowed composers to write truly horrible garbage with an air of superiority because "you just don't understand it" if you don't like it. This seems to have been a largely failed experiment: there are things that you can do in a piece of music that are more beautiful than other things, even if there is some subjectivity in terms of exact taste.

Ironically, the current period of music is starting to be called "postmodern" music, but it's returning a bit to the harmonic aesthetics of the romantic period (not purely, it's mixed with music from around the world as well as jazz and pop/rock ideas) and innovating more around music production technology - like adding electronics to the orchestra and experimenting with microtonal instruments - rather than trying to innovate on the concept of harmony itself. I would assume that this is in no small part due to the influence of film scoring, which is largely considered pedestrian by hardcore modernists, on the new generation of composers.

By the way, I happen to like a lot of the modernist stuff that I am rejecting here, but I think that's more out of familiarity (through study) than anything else.