I think it very much depends on the sector as to what BYOD means.
For universities it means that students bring their own laptop and expect it to work with minimal fuss: connect to wireless, print, plug in somewhere to recharge. There's no attraction at all in a device without a screen -- the huge use of mobiles by students suggests that the screen is actually the important part of the computer.
For schools I wonder if you could take your idea once step further. The kids don't carry their computers around at all, but only the computer's storage (say, a Micro SD card). That storage is the boot device for a VM at both home and school. Add some simple software maintenance and I think this has some value and is worthwhile poking around with. The biggest problem would be Windows.
Business doesn't know what to do about BYOD, and they keep watering down the concept in the hope that it becomes something else. Unfortunately in doing so they lose the benefits of the BYOD approach, and loop back to the start of the process without making any headway. Increased BYOD by contractors and the lack of "enterprise mobile" means they'll have to grasp the nettle eventually. If only offering "outside the firewall" Internet with a certificate-mediated access (VPN or PKI) back into selected resources.