In many ways atonality was the inevitable direction that late 19th century Romanticism was moving in, with increasingly ambiguous tonality expressed by composers like Wagner and Mahler. In the early 20th century there was an explosion of new approaches and techniques which started from this basis and pushed tonal approaches to the breaking point and beyond. Composers including Ives, Stravinsky, Schoenberg, and others were all trying new things within the realm of atonality and while we tend to look back and map history into narrow movements and philosophies to suit our current thinking, I don't think there was necessarily such a "serialism period" so much as there was the Second Viennese school along with a bunch of other composers trying things out at the same time. And even within the Second Viennese school the approaches were distinct; Berg is known for being a bit more "loose" and romantic in his usage of 12-tone technique vs. the rigid formalist Webern.
Leaving aside the dubious assertions of what is or is not listenable, the reality is that art music in the 20th century became more and more fragmented as the entire music scene changed around the world. Minimalism was just one thing that happened after serialism. Even if we exclusively focus on music labeled "European Art Music" the 20th century was a period of incredible experimentation and exploration with many different approaches to tonality (and atonality) introduced.