The android phones that work with an app work the same way as the iPhone apps; they receive streams over the Internet from the FM stations that provide them. It's how I listen to FM on my iPhone. It has a huge advantage over "real" FM - I can listen to an FM station anywhere in the world. Not just within 20 miles of the transmitter. If I'm driving cross country I can listen to the same station all day, not just for the 15 minutes I'm in range of the transmitter.
The RF chip can receive FM signals, but only if they get to the chip. To do that it needs an FM antenna connection and an antenna. There is no connection to the antenna input to the chip in an iPhone, and no connection to the FM tuner connections and FM display connections in the chip. So without a total redesign of the iPhone there is no way to make the FM tuner work. In addition, an FM antenna is 30 inches long, so portable FM radios use the headset cord. It won't work with a Bluetooth headset.
Considering that you can buy a wired headset that has a built in FM radio for about $10, what's the big deal?