I've always liked this NPR story which attempts, but ultimately fails to answer the question: Why Do Some Songs Fade Out At The End? Lots of nice record industry trivia and arcana in there. But again, it doesn't really answer the question - everybody had their own reason for doing it, initially, and eventually it became a standard option.
I'm thinking of that because my iPod just pulled-up the Kinks doing "Death Of A Clown" during a BBC session sometime in the 60s. And at the end, while the Kinks fade the song out live, the announcer says
"And from Mr. Dave Davies it was 'Death Of A Clown'. OK fellas. Out with a nod. That's it. Fade it away. Very nice. I think it gives them a great sense of power to do that."
Me.ow.
I wanted to double check that NPR article to make sure there wasn't anything in there about DJ's resenting bands who put out records that faded out, because pushing the volume slider down is the DJ's job, dammit! There wasn't.
I like the bit on the the Beatles’ Live at the BBC album where they play “A Hard Day’s Night” and the BBC engineer doesn’t fade it. The boys start shouting “That’s where the fade goes!” and the host quips that they sabotaged the fade so listeners would know they weren’t just playing the record version.