This is a discussion I've heard somewhere else recently, although i can't remember where. In my opinion, it is an absolutely unthinkable idea. As many people have noted before me, we use writing everyday—it's a means of general, quick expression. As a graphic designer, I can't help but liken it to a common trend I see in the design world. As we've become SO dependent on computers to produce our designs in the past 15 years, today's design students are having a hard time grasping why it's important to be able to sketch. Now, I can't draw my way out of a paper bag, but I definitely know how to get my ideas out with a paper and pencil, and I can work a logo to perfection without opening Illustrator (I'm a graduating senior majoring in Graphic Design). Handwriting, like sketching for designers, is a necessary part of daily expression and communication. One would be handicapped without that skill. Penmanship does not have to be beautiful, so long as one can communicate ideas.

Secondly, if we were to stop teaching handwriting, the question becomes: should we teach typography? If, when handwriting was the only writing we did, we were taught penmanship, wouldn't teaching typography to computer-literate students be a natural thing? There is an interesting Typophile discussion about it here.

In my opinion, not only should we teach the basics of penmanship, but the basics of typography, as well. I don't expect the world to fall in love with type and become graphic designers, but if it would steer people away from Comic Sans, Papyrus and Arial, the world would certainly be a more beautiful place.