That doesn't work unless the server sends all 1 million results (say) to the client up-front. Otherwise, if you prefer results from example.com but the server only sends example.com results on page 3, your client has no way of showing you those results on page 1.
I think I've been misunderstood, in my mind the client sends all the details about themselves to the server, the server builds up the search results and send them back.
Yes, the server has access to the information the client has, but it doesn't have any way to confirm that's true. It also could avoid storing that information all together if the client sends it again every time
