At one time the Guess Who did a live fade-out of their hit Clap For The Wolfman.
The original releases of ‘Not Fade Away’ by Buddy Holly & The Rolling Stones both fade away.
The Oasis song ‘Fade Away’ doesn’t.
That’s the kind of trivia I like! 
And double the suicide rate.
On the other hand, the relatively obscure Blotto song “Metal Head” has like five (non-fade out) endings. I think it uses every one of the standard rock endings. But they are making fun of the genre.
Kiki Dee’s “I Got the Music In Me” has like four endings. Just when you think it’s done…nope still going. I don’t think they are making fun of anything, I think they were serious that they thought that was a good ending.
I always thought the fade out was because inexperienced songwriters didn’t know how to tonically end songs.
“One of my private pet compositional hunches about the Beatles is that they preferred the complete ending over the fade-out more strongly than the average band of their period. Unfortunately I don’t have at my fingertips the actuarially global statistics needed to prove such a point; it remains a gut feeling for me. Indeed, if the “Rubber Soul” album itself were any indication one way or the other, its fifty-fifty showing in this department would seem equivocal.”
Then they ruined it all with “Hey Jude”…
I used to hate this song, Teardrops by Womack and Womack, because it doesn’t really begin, or end, it just exists and then drones on with barely anything interesting happening in between.
First song that came to mind for me was Moving by Supergrass from 1999.
This single data point proves nothing, I just wanted to link a really good tune 
The first thing that came to mind was “The Partridge Family.” On the TV show in each (?) episode they would be playing a song for a rapt audience somewhere. Of course they were merely lip-synching. When they got to the fade at the end, everyone suddenly burst into applause before they “finished.”
Wow. You’ve heard of Blotto! I went to college with Blanche.
“They’re Coming to Take Me Away, Ha Ha” ended with a fade out, as did “Honey.” So it was being done in the 60s.
And then there is Helter Skelter with a complete fade out, a fade in, then another fade out that is interrupted by Ringo’s “I got bisters on my fingers!
I once did a thread about the best fade-out guitar solos. Steely Dan did it often and the best. I really want to hear what was happening after the fade out. The two that come to mind are Skunk Baxter playing on “My Old School” and Steve Carlton on “Kid Charlemagne.” In particular if you crank up the volume you can hear the most interesting part of Carlton’s solo right before the music disappears.
Rachel Bloom’s “We’ll Never Have Problems Again” ends with a live fade-out on the words “live fade-out”:
Interesting. In the context of a club DJ where maintaining the beat between songs is paramount, it seems like the fade out would make it easier. But are you more at risk of losing the audience, say if you let the ending song fade too much before bringing in the new one? Seems like the type of songs that tend to fade out are more likely to be slower and less “clubby” to begin with anyway. Conversely, I can also see how a hard cut would make it more difficult to blend, so in that case I guess you’d have to line up a very similar song to follow, if not one from the same artist/album.
Radio DJs don’t have those same constraints. I know cross-fading between songs was very common for a while to prevent radio piracy, but that’s not really a thing anymore. I can see how that might still be done to reduce dead air on a long fade-out rather than just clipping it. Is it still common practice especially now with radio playlists being centrally pre-curated and out of the control of the local DJ (if they even have a local DJ anymore)? I haven’t listened to music radio for about a half decade now because I just got so sick of the repetitiveness and commercials.
I’m sure it’s not exclusively an 80s thing, but I think it’s fitting to note that the theme song to 1984’s The NeverEnding Story fits this pattern, of not so much “ending” as “fad[ing] away.” So maybe not “false advertising” after all.
Back in the 60s a local DJ went on an anti-fadeout campaign by interrupting them with various classical endings. Holst was a favorite.
Don’t hate on the fadeout on Hey Jude. That was always the last song at our junior high dances, so the long fadeout let you know it was your last minute of holding your date close (at least until the next dance).
Speaking of fade outs…
