Don't get me wrong, I do think it's bad that writing things by hand is becoming more and more rare all the time. In particular, handwritten letters and notes have an extra bit of "personal touch" to them that can make them very valuable to the recipient.
However, from the time I was in High School to today I would never want to be required to write a paper, well, strictly on paper (from the beginning). I want all of that ability to quickly edit at my fingertips.