"Hey, can I borrow a piece of paper?"
"Sure, just grab a page out of my teenage daughter's journal that she's not using. Flip through until you find one"
Here's an idea, privacy first, ooooh anit we cool coders second. Privacy very much has to be the default, not google's cleverness or revenue stream.
All I can say is thank the non existent one that I don't use gmail for anything even vaguely important.
The only reason you don't have the same reaction to the location bar in your browser showing browser history is that you're used to it.
If you don't want email results to show up on your search page, just don't turn it on.
If that is true, why would you expect every site to assume you want privacy, when you chose to have customization by being logged in?
If you're using multilogin, you're sending cookies for multiple sessions on each request. How can you blame the server for thinking you might want results for both?
Them: "Hey dude, can I use your computer real quick for a second."
You: "Err, hold on a second, I need to do something..."
Them: awkward silence
But more seriously it really depends on what appears in that search results and for which queries. If it's done properly it only triggers when there's a very relevant mail matching the query, which would be unlikely from just a casual search from a friend.
Also if just the title is shown, it doesn't reveal much.