I see a problem tho, the floppy don't go nicely with the car enviroment and they will probably become unreadable pretty fast.
I had a similar idea but i wanted to embed small nfc tag into some floppy disk and use a broken floppy reader that i own with a tag reader inside the gut of the reader reusing only the eject mechanism and the led, (i will be missing the nice motor noise tough...).
I'm also experimenting with other cartridge-style meccanism
Echoes of FlashPath (have one somewhere):
https://en.wikipedia.org/wiki/FlashPath
It is an adapter that takes flash cards (e.g. SmartMedia) and can be used in 3.5" drives.
I planned to do that with old 64 MiB or 128 MiB SD cards and a car radio with SD support: One SD card = one album.
However, nobody still makes SD cards this small, and using a 16 GiB card for 1 album seems wasteful :)
But floppy disks would be much nicer.
It would amuse my friends on car trips, not that I have any of those...