A distributed network of cooperating independent crawlers and indexers would be cool though.

If you want to search "privately", Search Encrypt will allow you to do so. Bing, however, tracks users and links their searches to Microsoft accounts. We also have expiring browser history so anyone with access to your computer will not be able to see what you searched for.

We explained how this works in this post: https://blog.searchencrypt.com/tech/remove-search-encrypt-ex...