Re: 2 screens
You might want to avoid driving a car then. Checking your mirrors may prove to be equally challenging.. ;-)
Speaking of which, I recall Sony had a stab at this, using the PSP as an auxilliary screen for the PS3? Don't think anything came of it though. Only example they came up with was the above - using it as a rear-view mirror.
The only advantage I can think of having a personalised screen on the controller is during multiplayer split-screen games, where you have no private information available. On regular consoles it's trivial to see at a glance exactly where your opponent is and what they're doing.