This was tried with WiGig, and that didn’t solve any problems significant enough that it caught on. People tried to use WiGig for things like wireless docking stations, and I suspect it just wasn’t needed because at such short ranges, most people would want/need to have a power cable connected (which naturally leads to the USBC docking stations we have today, where both power and data go over the same cable).
Wigig wasn't fast enough to be useful for wireless HDMI, especially given 4k displays arrived right at that moment, and 2nd gen WiGig it's probably way to expensive.
The question is whether it's possible to create a full-rate 224 gbps transciever that is cheap enough to appear in mid range phones, notebooks and TVs and whether it would work without line of sight, but in the same room, with reflected light.
The wireless adapter for the HTC Vive headset was based on WiGig. The range is limited to a few meters, but that's more than enough for room-scale VR. The need for massive bandwidth and low latency make it a perfect use case for WiGig.
WiGig just came too early, the underlying tech was also barely able to support it. Windows 7 and Vista era, expensive and the software really wasn't there either.
It might be different now with VR and the rise of docks.
