EDIT: It appears that at least one person disagrees with me. So, a quick question: Which takes more effort for the end user, switching to a new search engine or switching to https?
I can tell you that normal people who care also don't know about HTTPS or how to use it. I'm all for Google making it easier to do so, or otherwise stop this personal information from leaking. See http://news.ycombinator.com/item?id=2122431 for some ideas.
Also, FWIW, HTTPS alone doesn't solve the issue completely, as HTTPS->HTTPS traffic still leaks.
If you don't want referral headers to be sent from one website to another, use HTTPS, or turn it off in your browser.
The best would be to just prevent ad networks from collecting this personal information altogether. The only reason I've heard against doing so is that webmasters need search terms for SEO, but they can get them via Webmaster tools.
Failing that, they could make a setting in the http version that turns off the headers. They could also make a setting that defaults to https. And they could make https easier to get to. Currently you can't even do https://google.com/ (you have to type in www.)
And so could Microsoft, Mozilla, Apple, and Opera.
As others have mentioned, this is a good marketing move, but it's not clear to me that you actually care that much about this issue.