Through this same mechanism wouldn't the advertising networks be privy to the content of the sites that I am visiting? It seems that even if we eliminate this, we still have issues with advertisers being able to track and create a profile based on the content of the websites you are visiting.
The headers do seem to create a direct link between a given search and a set of visited sites, but can't things like cookies and tracking pixels be used to the same effect? Possibly then using NLP to figure out the most important words on the page? Or the SEO terms that the website uses to get picked up by the search engine?
If you are going to let an advertiser post content on your site, it seems to me that it would be very difficult to keep said advertiser from tracking your users.
If the user uses Adblocking software or otherwise blocks the advertisers' sub-domains, does the advertiser still receive the referral headers?