There are no technical reasons why this isn't done. But there are legal ones. Most folk are not ready to accept the legal issues. That is, they think it's a dumb reason but Comcast and the content suppliers are very concerned about content "leaking" outside of where they want it to play.
That said I own a ChromeCast and a Wireless HDMI system.
I have a Samsung Smart TV (PN60E550) connected to my wi fi network with Samsung's Allshare application on both my TV and on my PC. I am able to view on the TV most video files that I have installed on my PC. But is there a way to send a video that is being viewed on the PC to the TV in real time. An example would be the last Dave Letterman show that I can access and view via Comcast's Xfinity on my PC but have no way to send it to my large screen TV.
The Letterman show I refer to on Xfinity has no way to save to file or share feature.
Any suggestions would be appreciated.