If you've had a strait forward natural birth, they will discharge you as soon as the baby is checked out by the pedi.
For those of us NOT in a private room, you want that to happen asap...let me tell you (from experience), sharing a room with three other moms and their newborns is hell.
I'm sure Kate could have stayed longer, but am guessing she has a baby nurse waiting at home to help, so if everyone is healthy, no reason for her to stay.