Still, not cool. It is not uncommon for someone to use my machine for a brief stint. Say we're about to go somewhere and I ask them to print the directions. I'd rather not have emails from 5 years ago pop up in an innocuous search.
If you use Chrome, just CTRL+SHIFT+N (or CMD+SHFIT+N) and open them in their own session that auto-expires when you close the window. Then whatever they're doing is safe for them and they don't kick you out of all your accounts. And it takes a fraction of a second to do.
"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"
"protect my privacy" is a really poor way to position this argument, if only for the many times we need to take companies to task for actually violating people's privacy. This is showing something on screen that you'd rather only have shown in a different tab.
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.
Privacy-first would be logging out of sites when you're finished, or having the default state of your browser to be un-authenticated (just use private modes everywhere). If you don't do either of those, then you are clearly not using the options (easily) available to you to be private-first.
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 can do that, you may as well do the thing you were going to have the other person do. I think notregistering is referring to times you may have your hands full and/or can't get to your computer.
And it's not just when someone else is using your computer. At work, I frequently have people in my office asking me questions, and I often do a web search while they're sitting next to me. I wouldn't want personal stuff from my e-mail being displayed to random co-workers. And I really don't want to have to remember to open an incognito window for searching every time someone is in my office.
Why not just have them log in as a guest? I haven't used other OS'es in a while, but on ubuntu that takes 3 or so seconds. That's a best practice you should be doing anyway even if your emails were not showing in search.
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.
It would be interesting if Google provided a switch in Chrome/ium to allow you use Incognito as the default mode, and Ctrl-Shift-N to pop up a normal window. That would mitigate this scenario somewhat, at least on one browser.