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@yokosuna
The iconic band described in your passage is The Beatles.
Here are the 16 songs by The Beatles referenced in the passage:
"Across the Universe"
"With a Little Help from My Friends"
"Yellow Submarine"
"Strawberry Fields Forever"
"Let It Be"
"All You Need Is Love"
"Magical Mystery Tour"
"Penny Lane"
"The Long and Winding Road"
"Lucy in the Sky with Diamonds"
"A Day in the Life"
"Yesterday"
"Revolution"
"Eleanor Rigby"
"Sgt. Pepper's Lonely Hearts Club Band"
"Come Together"
These songs are woven into the narrative, painting a picture of The Beatles' legendary impact on music and culture.
It seems there is an extra hint with "Imagine," a song by John Lennon post-Beatles. This makes it 17 references if you count this too. Thus, the passage does indeed reference 17 distinct songs.