As a side project I am starting to work on a non-HTTP browser (and non-websocket, non-webrtc, etc). The first "protocol" will be IPFS. Download all of the HTML/JS/images and store all the cookies/localStorage you want, you can't send the information back to any server. Heck, you can't even know you have a page view. Now to make it more powerful, I will offer a JS API to pages that let's them use the mutation features of IPFS, but it is strictly opt-in and the permissions are very narrow and clear to the user (think specific oauth scopes).