Would it be impossibly difficult to invent a way of storing/playing sound in analogue form that is more efficient than a record deck or tape? Or is it all about the record deck/tape player?
Starter for one: Laserdisc.
Analogue, most of the advantages of CD, phenomenally higher bandwidth than vinyl or linear tape.
Obviously you'd have to invent a new standard for encoding high-quality audio - the existing laserdisc standard modulates the audio in with the composite video, which is never a good idea (there's also PCM digital audio, at the same spec as CD).
TBH, you could do a half decent job with FM audio on VHS. I'm sure a helical-scan tape system would work even better without a video signal cluttering things up.