>> If you do it checksum based the checksum is embedded at the place where the asset is referenced from which is an encrypted page
So you are still loading an encrypted page from somewhere? This scheme gets more complex by the post! I think by extracting this idea from your head piecemeal we have confused me!
Let's see if I have this straight -
I browse to https://www.example.com and get served a page that is authenticated and integrity-checked, but not encrypted. Probably via TLS in NULL cipher mode. Embedded in that page are simple sha2 (sha1 is bad, collisions may be possible) hashes of all the images etc that I need to load. The CDN provides these and I can verify the hashes against what I'm expecting.
OK, you've removed protocol overhead on the assets (if they are binary assets this is likely a very small percentage). And you've removed encryption from everywhere. This allows people to get a verified page that's not secret. There's no reason I can think of this would not work. You're still having to give your private key to any third party cache/front-end that serves your HTML.
At this point we're down to an idealogical argument - I think crypto-everywhere is good because I prefer as little information as possible to leak to any interested parties, regardless of how sensitive it is, and because using crypto on everything helps to hide the important stuff. You would rather some things be observable, and don't think the overheads are justified. This we are not going to resolve :)