DAT was popular in the jam-band-taping community around the time this device was released. Folks would go to shows, and either record the show with their own mics and tape deck, or by plugging a line directly into the soundboard and then taping. I think back in the 70s, people used reel-to-reel tapes, and many tapers upgraded to DAT (IIUC, not very many used regular analog cassettes). Tape copies were distributed in a tree fashion and each generation was degraded compared to the original.
I wasn't able to do DAT because of the extremely high prices. So I mainly ended up with copy-of-a-copy-of-a-copy analog cassette, which usually sounded terrible (lots of tape hiss and distortion).
Analog cassettes had their own issues: dual tape decks made very poor copies (I think this was some sort of copy protection feature) although you could use two decks. I was really glad to see analog go- these days, nearly eveyrthing is digitally recorded, with all the conveniences of digital, and many old reel to reel tapes and DATs have been captured with high quality devices.
It's also kind of funny that I lived through the entire CD era- from the first obscenely expensive CD readers to an age when everybody could buy a cheap blu-ray recorder to CDs being obsolete.
Some soundboards had a tape recorder built-in, so you could give the guy running the mix a blank tape to hit record when you started playing.