[audio cassette player] Are both or only one "axis" supposed to drive the tape?
(piefed.cdn.blahaj.zone)
Yes. In very rare cases, vinyl records will be cut with tracks running inside to outside. In the one example I've seen, it's to accommodate the building crescendo of the classical piece recorded. The louder more dynamic portion at the end benefits from the faster vinyl.
https://m.youtube.com/watch?v=5Afikv6k1-c
Edison's original phonograph used cylinders which offer constant speed playback.