Anyone who really cares can - and will - use HTTPS.
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.
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?