A remote kernel, with local storage, would be interesting. No need to worry about viruses, since there is no local OS to infect, but your data could still be fairly secure residing physically on your own computer
That’s not how it would work. Everything would be remote hosted. Your local machine would not have any storage. It would be akin to a WYSE terminal with network connectivity, USB ports for peripherals, and an HDMI output for your monitor/TV. Everything’s in the cloud.
Even in your example, however, all that’s required is a kernel-mode exploit to sniff all of the channels into your processor, and your data is no longer secure.
Microsoft’s already going “to the cloud” with Office 365 in the business world. All of our email is stored on MS servers with remote hosts handling all mail exchanges. This is an end run for Microsoft to finally get what they believe is theirs and no longer have to worry about losing money to licensing for their Office products. The next generation of corporate desktops will be hosted by Microsoft. Mark my words.
I seldom use a PC without access to an electrical plug, even my laptops.
However, I can't imagine not being able to do real adult work on a PC in environments, which I have often experienced, where there is no access to the internet.