The TV doesn't have to be blank while you do this. You could be searching on the phone and seeing results (best for the searcher), and the TV could solely show results (as opposed to half the screen being taken up by a ridiculous keyboard). Best of both worlds.
I have a boxee and I'd been thinking about how to implement this for a while.
It seems like it should be possible to have a box act as a web server proxy where it mirrors a web page to several displays.
It would be pretty slick if you could get a simple http proxy to support screen mirroring like this, because then it wouldn't matter what combination of set top box / phone / tablet you have... you could mirror anything.
