Ironically, the inability to cache TLS on the edge of my network makes the Internet more surveillable since everything has to pass through the Room 641As of the world and subjects us all to more network behavior analysis. The TLS-everything world leaks so much more metadata. It's more secure but less private.
You can do it if you're happy to deploy your CA to your network, can't you? Deploying CA certs sucks, though. I wish it was easier.
Yes, that's a real problem. Probably moving to a content-centric networking or named-data networking system would help with it, while also creating difficulties for censorship, and IPFS and Filecoin seem to be deploying such a thing in real life as an overlay network over the internet.