Even if the TEMPEST were easier, it's significantly less powerful, as it's not going to get you the ability to write malicious firmware to the audio device nor a persistent connection to the host device when the audio device isn't connected.

I doubt that audio-spectrum RF/magnetic frequencies emanate strongly from wired headphones. They are simply not a long enough antenna at 200-3,000 Hz. Also, the loop area is quite low. The ground wire runs parallel to the L/R wires, so the only loop to receive is the magnetic coils in the headphones, which are small. Only near field would work, IMO.

Thanks!