Good video compression takes a lot of time/processing power. You need to do multiple passes over the data, calculate motion vectors etc.
You can do realtime compression, but you won't get close to the same compression ratios so you will need more bandwidth.
Even 'realtime' compression takes time so would probably introduce an unacceptable delay between the computer and the screen which is very disorienting even if it is only a few tens of milliseconds as the mouse pointer no longer feels responsive.
RDP/VNC compensate for this somewhat by suppressing the drawing of the pointer on the remote screen and drawing the local one over the top instead.
This would not be an option for a wireless screen.
It would also cause AV sync issues when watching video.
Realtime compression of an HD signal would require a lot of processing power, which would mean your tranceivers would need to be mains powered and fan cooled.
If any wireless technology is going to 'fry your brains' it would be one that attempts to reliably transfer 10GBPS over 30 feet using UWB or something.
In short it probably isn't worth attempting to do this until it can be done via quantum entanglement or subspace, that is to say many years into the future. Except by then we will have Mega High Definition screens which will require even more bandwidth.