Not the same thing as hiding your IP and the domain name, but we're getting closer to full privacy, slowly. The problem with proxying is that it would only work with a small list of third-party asset hosts, and it would break the ability for CDNs to work unless it was a distributed proxy... that sounds like more headache than its worth except maybe as a new type of browser extension, something similar to a content filter but instead loads cached or proxied copies.
But at that point it's worth considering VPN or compression proxy services for content compression as Chrome and Opera Mini might do, and MITM everything the browser loads so nobody gets your IP except Apple. I imagine folks might pay for an Apple VPN service, I'm just not sure Apple wants any headaches that might go along with it yet. :)
Why not just remove referrer header for all 3rd party requests? Or remove it in Private browsing mode. VPNs nice, im using one, but other VPN companies are not, such a cutthroat business :) And you can not self-host VPN, it defeats the hide my IP feature.
https://caniuse.com/referrer-policy
Hoping the defaults for sending such metadata will change eventually
https://www.zdnet.com/article/firefox-to-ship-network-partit...
But evil servers don't.
Example: gravatar.com gives an expiration time of 5 minutes.
curl -q -i --output - https://www.gravatar.com/avatar/70d9b050bfe39350c234d710fadf... | grep -a xpires
expires: Fri, 12 Feb 2021 11:54:40 GMT