The benefit of taping a piece of paper to the wheel is that you could apply the same technique to something like a treadmill where you wouldn't want a magnet to be traveling along with the tread. The benefit of Arduino is lack of OS overhead/risk.
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.