This is the stated reason why Microsoft uses their proprietary wireless standard for Xbox controllers (which have Bluetooth, but not for the Xbox console itself) and headsets - but I haven’t had latency issues using bluetooth headphones on my PC.

Now, I know that in a lot of cases, Bluetooth doesn’t have the bandwidth necessary to do high quality bidrectional audio - so it can’t receive and send audio (microphone) without falling back to a very low quality profile, which results in cruddy audio. Not sure if this is an issue that has been fixed though. If not, I can’t imagine anyone would want to game and participate in voice chat using that as it sounds horrible.