There are a lot of interesting ideas that you could put together when everyone has a private screen. I wrote up the cons and pros of having such a system and where the innovation will come from when I was looking at tablets as the controllers:
The Gamecube already had private screens with GBA adapters.
In Crystal Chronicles each player had their own menu, a secret competitive challenge (in an otherwise cooperative game), and a unique view of the area (one gets a map, one gets a dot for every monster, one gets a dot for every chest, one gets information on monster attributes).
Four Swords also used the GBA screen, but it was basically just so you could go in a dungeon and wander off without splitting the screen on the TV or making you stay together.
There were probably more games that used GBAs for private screens or other multiplayer gameplay, but I cannot recall them off the top of my head.
https://github.com/icefox/tablet_tv_games