And it's not even about only headphones. It's about billions of audio devices that take one thing as input: line-level audio. Home stereos, car stereos, portable amps, hotel-room docks and TVs, PA systems and mixers.
Then there's the idiotic problem that Apple created but never even solved: blocking the phone's sole port with a "headphone dongle," which prevents you from CHARGING the phone. So now if you want to listen to music while navigating (which kills the battery quickly), you're screwed.
I ended up buying a few of the Lightning-to-30-pin-iPod adapters, which you can then plug a USB+audio cable into. Yes, the ancient 30-pin iPod connector has line audio out, and the cool thing is that it's a true line out; the volume control has no effect on it, so you only have one volume control to dick around with (the one on the amp).