The reason for reuse isn't really the cost (though that's certainly part of it). The main driver is that they are going to become the production bottleneck if Falcon 9 reaches the flight cadence they are shooting for. The fairings are a big, unwieldy shape, and they take up a lot of room during the manufacturing process, so they can only make one at a time.
If you saw $6 million, falling from the sky, would you try to catch it? Each fairing is around $3 million, so they're trying to catch it. That gives them $6 million more per-customer they can discount the price should they need to get really competitive. It is really kind of insane that no one has tried this before.
Here is Musk using it in regards to saving the fairing @ ISS Research and Development Conference 2017:
https://www.youtube.com/watch?v=5cPMS6cT0Ig&t=825
In regards to the first stage (booster stage) at Code Conference 2016: