The god thing about encryption is that it hides your data from some else's eyes.
The bad thing about crypto, is that the eyes of the caching servers are now blind.
Content Delivery Networks
CDN are commercial networks of servers all over the world whose only purpose is to cache and distribute your data as quickly as possible.
If that data is encrypted, the CDN will not be able to cache or read anything.
So the first commercial CDNs asked you your public and private keys, the full X.509 certificate. they basically impersonated you.
And you could do nothing but trust them.
Of course, this is ridiculous, so those same companies modified webservers and TLS libraries so that you could kep everything on your servers, but once the key agreement ended, you had to send them the generated key.
And they would effectively Man In The Middle you. You still have your keys, you still have to completely trust them.
I have a (unfinished) proposal for a secure proxy. The basic idea is:
programmers mark each cachable data.
the data is sent and stored (encrypted) in proxies, with a cleartext identifier of the resource stored.
the client gets the data from the proxy, but the key from your server.
The proposal is still unfinished, as I am ironing out the definitions and interactions of explicit and transparent proxies.
In this CDNs are not strictly considered yet, and I will have to include that, too.
So a lot more work here, but a protocol-level secure caching proxy/CDN mechanism? Who would not like that?