Well, diamond is harder, but its not harder enough. 9 mohs to 10. You need the aggregate diamond nanotube files, or it'll be like doing stainless steel with hardened steel. And that just wouldnt do. Plus, I want fancy super-material tools!
I dont think carbon nanotube strings would vibrate very freely. Now, a nanotube through neck, where the nanotubes are normal buckyball width, but each one runs the full length of the guitar: that would be a hell of a neck. Certainly wouldnt drift. Or need a truss rod. Or need to be more than 0.0001mm thick.