Why not air-dry knives? I've read that one should hand-wash knives, and I mostly buy that. I've also seen advice that one should dry them immediately and put them away. 

Why shouldn't knives air-dry? Aside from the unsightly water stains, is there any downside to letting knives air-dry? 

Edit: We have Henckel full-tang knives. Rust is a real concern -- we had them sharpened, and the shop did a lousy job -- the edges are ragged.
It's to prevent rust. Rust requires oxygen and water to form. The longer you leave your knives wet or damp the more likely you are to develop rust.