For music, it is clear that loses quality with Bluetooth and to be honest I've never tested the headset by plugging the cable Jack-Jack. I do not know what it is wired but what I wanted with this helmet it was just not having a cable node into the bag.
There is one thing that I find harmful, it is the absence of lock button. It may indeed happen that the headset turns itself if it is a bit compressed in such a bag.