So the term hosting may be technically inaccurate here. However the practice of deploying sites entirely behind CloudFront recently got much easier. The change came in this announcement that CloudFront now supports POST requests. A long time (years) in coming, this now gives options to sites that would like to have quick setup with a CDN and have lightening fast sites with minimal setup. I'll post more soon on how to do it but it's great to know that it's possible now.