Why? To have all your computing stuff with you all the time. That is not just your documents, but your programs and settings. And to only maintain one system. They way i see it, the only rival to this vision is the cloud, and there are a lot of issues there[1]

Battery isn't going to be a problem either. With today's solutions you could just plug in one cable which connects to the monitor and charges the phone. Tomorrow- your desktop will have a surface to put your phone on that will charge it (like your toothbrush charges), perhaps authenticate with NFC, and then connect to your display with WiDi or similar, and your keyboard.. yes, seamlessly. Another thing you will have gained is you won't have to buy a second device. Of course, we here are likely to be the last to give up a computer-proper.

[1]: other than the obvious trust, reliability and privacy issues-- there is currently no solution for most applications-- licencing issues? many companies are likely to drag their heels here. And when there finally is a technically perfect and complete solution; how are you going to pay for this? advertising, $, or selling your data. Or, you could just keep it in your pocket, yourself.