>Technology is where it is today and I am wondering why do we still have to plug a HDMI cable from the tablet to the monitor to get the image. Why isn't this wireless? Or, is this technology already avaiable? If not, what would make it not possible?

Is available in Google Chromecast.

Cables are not bad IMO: anything on air is easier spied upon. I have no opinion on bad side effects of more radiation on human bodies, but the benefit of loosing cables is not that big, so for me cables if possible ;-)