Wired headphones get power from whatever they are plugged into. Once you decide you don’t want to physically connected to the grid while wearing the headphones

Wired headphones get power from whatever they are plugged into. Once you decide you don’t want to physically connected to the grid while wearing the headphones, you’re going to carry a battery around (or generate power with solar or something). If you’re also carrying some additional device (eg. a phone or mp3 player) along with the headphones and you’re wired into that device, you could have that device handle the power. Nowadays I’m frequently switching my listening and speaking between different devices, some of which are on my person and some aren’t. So plugging the headphones whatever I’m currently using would be inconvenient and restrict my freedom of movement. Therefore it’s nice to have for the headphones to contain their own battery and do automatic switching between different input devices. Solar sounds like a gimmick to me, the battery life of the headphones is not any issue anymore.