The lack of this feature is going on still.

I'm using a 3.5mm jack headset, and like the OP, I can't just switch the sound setting to my desktop and have the sound come out.
I actually have to close FFXIV client to have my sound come out. Quite...no, VERY annoying.
Before I came to play FFXIV, I was playing WoW, and they already had this feature N years ago.
Would appreciate if this feature gets implemented *soon*.