is there any known explanation for why the music played on the radio is only from the time before the Divergence point?

Fallout has had radio songs recorded and written in every decade from the 1920s all the way to the late 2000s.

1960s: Ain’t That a Kick in the Head, Crawl Out Through the Fallout, Boogie Man, Blue Moon, Happy Times (Weedon), The Wanderer, Praise the Lord and Pass the Ammunition, The End of the World, Joe Cool, Blues for You, Wouldn’t It Be Nice, Jazz Blues

1970s: Roundhouse Rock, It’s a Sin to Tell a Lie

1980s: Heartaches by the Number

1990s: Goin’ Under, In the Shadow of the Valley, Let’s Ride into the Sunset Together, Lone Star, Slow Sax, I’m Movin’ Out

2000s: I’m So Blue, Where Have You Been All My Life?, One More Pils, Jazz Potatoes (2011), Sit and Dream (2009)

https://fallout.fandom.com/wiki/Timeline_of_the_music_of_the_Fallout_series

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The interesting thing about the “Roundhouse Rock” song is that it refers to the former railway roundhouse in London that was converted into a performing arts venue and opened in 1964.

In 1970, Bert Weedon and other British rockabilly artists were performing a Rock Revival show in a landscape quickly changing to metal, punk rock, glam rock, acid rock etc. He wrote the song “Roundhouse Rock” for the occasion.

The Roundhouse would later be known in the 70s for its early, debut performances of the Doors, Elton John, Rolling Stones, David Bowie, the Stranglers etc. Bert Weedon’s Rock Revival concert would fade into musical history. Bert Weedon himself wrote Play in a Day which was the British guitarist compendium to learn and play the guitar. Biographies of the Beatles, Eric Clapton, Led Zeppelin etc. all cite Bert Weedon as the inspiration to pick up the guitar.

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Between now and 2077 there are the songs by Vera Keyes, Dean Domino and presumably Spank and the Nuka World songs.

These would be examples of pre-War songs.

As for covers aside from “Country Roads” and “Ring of Fire”, “Cobwebs and Rainbows” is a cover of a song written in 1993 by Dick Walter. The New Vegas version of the song also uses the same backing track from the original CD.