Well, yeah, handwriting is rather important, and necessary. At least until we invent the telepa-pen, which instantly scribes your thoughts for you. But to be honest, that kind of technology probably makes written language redundant.
Eastern hand writing is a little different from Western though. In the West we don't really care how a letter is made, as long as it vaguely looks like one. In the East, the rules are a lot more rigid, with even the correct stroke order necessary for each character, particularly with Chinese.
This was fine when writing was limited to a select elite, but recently it's become a much more basic part of life. The Chinese government tried to address this and make things simpler, hence the divide between the graceful flowing Traditional characters, and the angular utilitarian Simplified ones.
The problem these days is simply the proliferation of Roman characters around the world due to the internet. We had the same thing in Europe during early history, when the spread of Christianity pretty much wiped out the older runic style writings. In China and Japan, Roman script is everywhere.
Is it a bad thing? Probably not. But old dogs don't like to learn new tricks, and so of course there will be the cry of cultural destruction. I don't think so though. Already there is a divide in the internet language, even using the same alphabet. You only have to look at emoticons to see this

And I can't believe I spend so much time translating them for people orz
The future will see some startling changes in how we use our written language, but, ever the optimist, I see it as more of a natural evolution, rather than usurping local culture.
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So yeah, hand writing should still be taught in schools.
Kind of went off topic there...
orz