The problem is that Europe was always awful, involved in war after war, but the musical styles ranged from the happy Baroque through the Classical and Romantic periods then back to the Neo-classiccal(Stravinsky), then on to the modern hodge-podge of multitudinous styles, some good some bad, and some very forgettable.
There was nothing new about war in the 20th century, definitely, but the 20th century is unique because that's when we got uncommonly good at it. Take any war from previous eras... we can now duplicate that at the push of a button. It is revealing to compare the musical responses to the two World Wars: it's not surprising that neoclassicism came out the interwar period and Darmstadt avant-gardism came out of the Cold War. That is to say, it is not surprising that Straviskyan neoclassicism emerged out of pulverized France in the 1920s, when Stravinsky and his clique blamed hyperemotional German Romanticism for the war, and that they sought to set things right by "returning" to pre-Romantic genres (in theory; not that 1920s neoclassicism, in practice, resembled its supposed models in the least). In that sense, anti-Romantic composers still had some sense of optimism that there could be musical life after the worst war ever. It was much harder to keep up that illusion after 1945, when in spite of their efforts Europe still tried to annhilate itself in an even more horrific war; and so it seems equally fitting that the nihilistic avant-garde, of the kind coming out of Darmstadt for example, should be born out of the post-WWII era.
Of course, it would be too facile to lump all 20th century composers in this narrative; as you mentioned, there are notable exceptions. In previous threads I've expressed my admiration for Ligeti in this respect; I would say the same for Britten, Bartok, Milhaud, Messiaen, Rochberg, Saariaho and many others.