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.
Indeed. A cassette was a miniaturization and interface improvement over reel to reel systems. So it inherited some of their properties but added new ones (like the protective case) and lost some properties (like splicing or adding and subtracting length of the medium)
What I really want to know is whether the fact that a standard pencil could be used to manually wind a cassette was an intended feature or a happy accident.
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.