This is why my "gamer" headphones can use both profiles simultaneously! The game/music/media audio comes through the headphone profile, and chat audio comes through the headset profile. There's even the ability to change the volume-per-logical-device (chatmix).

Agree with you that I never got it working consistently in Linux. Just getting normal BT headphones to use A2DP rather than HSP was always a bit tricky. I've not dared try my gamer headphones...