They're going to get lost so fast
Getting your headphone cord all tangled up in itself is a pain in the ass, but removing a cord altogether poses some big problems. First of all, did somebody say choking hazard? Second of all, most wireless headphones on the market today are tethered to one another, both to improve audio quality and to keep them from disappearing entirely if and when one drops out of your ear. You can argue this makes them look lame, but they serve an undeniably functional purpose.
As the Guardian's Julia Carrie Wong so eloquently points out: "The beauty of the headphone cable is just like the beauty of a tampon string: it is there to help you keep track of a very important item, and help you fish it out of whatever nook and cranny it might have fallen into."