Spot on! I pity the resources we waste. It seems people have forgotten to respect the fundamentals of computing.
Why even bother running a web server? Just use S3 with cloudfront.
It looks like this would work, but you would have to use www.myblog.com instead of myblog.com since you have to use a CNAME to use cloudfront. Maybe using cloudflare's CNAME flattening?
Unless you host your domain servers on Route53, in which case you can configure an alias record at the apex.