What if, an idea that's just occured to me, what if PSP2 wasn't as much a handheld as a portable device, with a deliberate intention for it to be transported and connected to TVs? The idea would be a device that could play games to a respectable standard for TV output, Wii-ish low-performance tech for the masses, and read a Move controller, play 1080p movies etc. Such a design could compromise power efficiency for flexibility assuming a lot of the time it'll be plugged in at the wall connected to a TV and it'd give the handheld a new niche presence instead of competing directly with the zillions of handhelds out there and coming.
Edit : in fact, running away with this idea, what if the next PSP is designed to be pretty much bytewise compatible with PS4, intended as a portable PS4 experience. You're at home, buyt the latest game for your PS4, and enjoy it in 1080p. Then you drag the game from the PS4 onto your PS4P (PlayStation 4 Portable) and can play a cut-down version of the same game using the same save files, with the same internet connectivity etc., and can play it as a handheld. You can take that device to a friend's house and plug it into their TV to play the same game, cut down but still watchable, on their big TV, before finishing off with a movie on the HDD. That to me sounds like a novel experience that'd be marketable and desirable and offer some wortwhile competition to Apple and friends.