Oddly, atonality and aleatory music—both enjoying a vogue, among the elite, in early and mid-20th century—have failed to find any real momentum, even though they were viewed as contributions to musical "progress." In the meantime, earlier styles—from the Renaissance and Baroque periods, for instance—have captured the interest of serious listeners.
A few years ago I sat through a performance of Schoenberg's Gurrelieder, one of pre-12-tone pieces. It was long and boring. On the other hand, I like a lot of Ives and the little there is of Ruggles. There is plenty of modern classical music that is well worth listening to, but it doesn't get programmed - John La Montaine's Pulitzer-winning piano concerto, to name just one off the top of my head.