There are some advantages.. Really, the analog side of audio hasn't been improved for about as long as the mini-phono connector. Instead of relying on the underpowered, noisy, and lossy DACs inside the phone, you can push the burden of achieving higher audio quality to the headset, where there is arguably more room to place better hardware. You can also then put more pressure on the headset manufacturers to implement better audio quality, instead of taking an analog stream from the phone (which was already converted from digital), converting it back to digital to push some horrible convolution filtering on the sound (beats, ie), and then converting it back into analog to make it to the drivers.
Any audiophile will tell you that the best theoretical sound can be achieved by a straight wire with gain applied, which is technically impossible.. But this shows that the more steps you take out of the process, the better the sound quality is.