They didn't :-). The cursor -- a moving indicator, as part of a slide rule or any other similar instrument -- has been called that way since the early 17th century.
I think you're overthinking the whole thing, it's not really "on" a tape. It's the default operation of a tape, they didn't have to come up with the idea, it's a side effect of the medium. You need a motor to move the tape, no motor = no movement = the tape stays in its current position. To automatically rewind the tape you'd need some sort of mechanism under tension in it which would probably make it less reliable / more expensive.