Yep this is definitely viable for Arduino. You are right about the normal audio tape heads cant practically read or write a "1" or "0" directly. But the cassette deck takes care of all the details when recording audio. So make data into audio.
Back when the earth was cooling, small microcomputers began to scamper about beneath the feet of the big mainframe dinosaurs. A floppy disk drive cost over $1000 and we could only dream of someday owning a hard disk with 0.0001 GB capacity. We used a standards called "Kansas City" or "Tarbell" see Kansas City standard - Wikipedia
Something like this would still be the easiest way to use magnetic tape today.