Not necessarily a song, but a piece of music, or part of a larger piece of music if it's a movement of a symphony or such. The top ten 'artists' I have music for: Track Count Artist 3,758 Bach 1,662 Beethoven 1,161 John Williams (as conductor/composer) 1,003 A DJ who lets fans download his streams 894 Stravinsky 779 Paul Whiteman 708 Austin Wintory 562 Glee 558 Ron Jones 552 Jerry Goldsmith As you can see, that doesn't even get into Rock and Roll or Pop music.
That's of course the real reason. In-universe, you'd expect most people to actually care about the 20th century no more than average people in real life care about the 17th century. And among the few 'history buffs' that would be there you'd expect some to be interested in the 18th, others in the 20th, and yet others in the 22nd century. Unless of course, the 20th century stood out like a sore thumb in later history, a pivotal time somehow.
Well, having pre-Eugenics wars, pre- (official) first contact nostalgia is hardly surprising. Many secretly long for a simpler life, even if they're remembering it with rose-colored glasses. Even their adventures are simpler, with low-tech, and differing sets of skills needed.
What was that thing going around a few months ago about how often men think about Ancient Rome? Maybe the 20the century is like that. (I never think about Ancient Rome. I think about WWII CONSTANTLY.) Invention of powered flight. Computers. Mass media. (You can't listen to actual Beethoven or watch actual Shakespeare but you can listen to authentic Bing Crosby.) Beginnings of space travel. Nuclear power. This is probably as a side effect of being written IN the 20th century but the way the characters are portrayed I can see where they would see the 20th century as where much of their way of life was beginning.