That functionality doesn't exist today, so it would be a new protocol. One that would be almost as complicated as HTTPS, would be starting from zero as opposed to the 50% usage of HTTPS on the internet, would require new code to be written which hasn't been thoroughly tested for security issues and would provide inferior assurance to HTTPS. All for the sake of being "simpler."

With regards to signing content, this already exists in the form of code signing. Given the amount of software that isn't signed I doubt it would be practical for anything else e.g. blog posts.