Mini screen have been considered a major improvement for two+ player sport games. Where you might want to keep your play secret. It also opens the door to virtual card games; magic the gathering, strip poker, uno. It could also be used as a quick way to copy mp3 to the ps hand held. Or use a cd, the ps2 internet capability to set up an itunes like serves for the ps2 handheld. Or store your ps2 save on your hand held, to bring over to your friends house.
Blue tooth or airport are two other way the ps hand held could sink with the ps2. Just who going to want to drain their ps handheld batteries when their playing at home? Wouldn't they rather have it pluged in and charging? Plus the ps2 dose not have blue tooth built-in, so they'd have to use the ps2 usb ports for blue tooth dangles. Witch would be expensive. Plus blue tooth isn't any faster then usb, and it's posible to have wireless inferences. As for airport, expect player to set up a home network with a wireless base station may be too much to ask, consoles have always been about simplicity. Then their would be the add expense of purchasing the wireless base station.
Unforhcently I do not have the time to google around for all the ps2 handheld faqs. I think I herd about the ps hand held controller capablity from g4tv. Perhaps they have some thing about it on their web site.
btw there is also a a usb super rumble pack for the ps2, but it only works with one game.