There are lossless audio wireless gaming headsets. Astro A40 used Kleer, which is 16/44KHz stereo. And now there's also Audeze Penrose. It should be noted thou

There are lossless audio wireless gaming headsets. Astro A40 used Kleer, which is 16/44KHz stereo. And now there's also Audeze Penrose. It should be noted though, that gaming headsets have different priorities. They usually sport bulky design enabling bigger batteries, and low audio latency is a must, so whatever codec is in use it must work fast.