Similar here, and as I have written recently:
https://news.ycombinator.com/item?id=26532433I feel that this could easily be a user toggle-able option near the url bar - and that people could choose to send referrer and search parameters to sites they like - and I could understand certain medical terms and what-not maybe people wanting to keep more hidden.
I'm all for the browser taking control of this and giving the users options - love to be able to have the web site detect this and add a box saying 'hey would you mind sharing referral and or search term with us"
It really helps when trying to figure out if you should be adding more content for 'term-mainly-X-demo' might be searching or for sure should be adding more content for other terms people are definitely searching for.
I would imagine that many people would like to hide referrer for fbook, most of my sites I would think people would be willing to help with providing such info.
as far as webmastering and stats to try to help visitors - it appears google is keeping more and more data to themselves, and now firefox is making it less transparent too.
I see there is a link to the referrer policy for your site, but nothing about begging the user to include the info when visiting - oh well.
awstats and similar have helped troubleshoot and helped expand many sites for many years and now another nudge to install third party slow-ware google-stats.. I just, sigh.