> Maybe using an archive.is-like service that renders the static page (as an image at the extreme)
A lot of companies are starting to use "browser isolation" which is essentially what you're saying. A proxy runs between the client and the server, but it does more than just direct TLS streams - it actually builds the DOM and executes the JS. The resulting web page is sent to the actual client browser, which might send back things like mouse and touch events to the proxy, which will then update the page.
I think most companies are using this as a malware protection thing, but it does hide the actual client IP address and fingerprint, and I imagine it would make tracking very difficult.