re: Have you seen my phone?
I think you might be missing the point. Your girlfriend will watch TV using her core gadget.
The screens just become peripherals anyone can use.
You walk into a hotel room, and the TV links to it.
You get on a plane/train/car and the display mounted in front of you links to it.
You sit at someones desk and you get your desktop on their display / keyboard / mouse / whatever.
You give a presentation and the projector links to it.
You're going out climbing/skiing/biking, so you take a bulky ruggerdised display to link to it.
You're going to work so you take you thin, large screen, iPhone-esque handset to link to it.
You upgrade to the new 4G 8-core version, and all the other screens/peripherals still work.
Lots of practical issues (battery life mostly) others have mentioned. But a very cool idea.