If you are going with a visual piece of tape, then you could replace the arduino with a simple mobile app that recognised the tape via camera and transmits speed via UDP to the app. I wonder if the camera on a typical phone could keep up ?
Inductive sensors are cheaper, simpler and more foolproof; cyclists have used them for decades to gather both wheel speed and cadence.
Also, Apple would certainly include a Lightning->Headphone adapter that would also be usable for card readers. They just use the line in from the microphone.