I'd say a lot more here.
First, students don't get to carry around laptops, etc., until they go to university. Junior high and high school students still write their homework by hand, unless it is specifically related to PC class.
Also, there are still a lot of paperwork (esp., forms to be submitted at the city hall, banks, etc.) that must be written on the spot.
There are still many older people who don't like to type on the keyboard and still write private letters, etc., by hand.
On top of all these, handwritten messages and letters are regarded best and warmest. A lot of people write New Year cards to friends and family by hand. Nice handwriting is still regarded a reflection of cultural refinement.
It is mostly in the adult world of business, research, etc. that most things are typed.
Added: I forgot to add that people in general are starting to write by hand less and less, especially because of cellphone use. But it still doesn't make you free of handwriting. Admittedly, I write less and less by hand and am starting to forget the correct stroke orders but am required to be able to read handwritings and write by hand as an adult Japanese.