What if it was to attack Google's Chromebook. Here me out. What if this little machine had only enough storage space for the OS and a couple apps. Or enough for the OS and enough iCloud that could hold the apps that people used. Put everything on iCloud. iTunes in the Cloud, Work in the Cloud, Calendar, etc, etc. It would need like 8GB of storage space for the OS and that's about it. And put 2GB of RAM, which is incredibly cheap now.
Using a old Sandy Bridge, I think that Apple could do it for $799. Will they? Probably not this year, I can see them moving this way in the future though!
Not Apple's style; that's a stunt more characteristic of most of the other OEMs. Even the iPad is more complete than the type of rig you describe here without the limitation of being a clamshell form factor. Everything you describe as the possible use for such a version is already available for the iPad at an even lower price overall.