Well, notes taken in a traditional spiral paper notebook can easily be converted to electronic form using a scanner...a scanner less expensive than an Edge, that can easily be shared by a family (assuming the school doesn't have one for students to use for free). Documents created in this way won't be searchable for text, but neither would those on the Edge.

On the question of typing vs. writing, I suspect that neither involves much brain activity devoted to muscle movement for someone who is experienced at writing/typing. Drawing unfamiliar mathematical notation, diagrams, "idea maps", or graphs probably exercises more of the brain due to these being less automatic, so you've got a point there...though there are some specialized pieces of software that allow you to do these things using just a keyboard (though learning how to use such software might force more of the brain to light up as well).