I think the only way others cannot search your post history is when you become a guest by having your account deleted by request. I suspect this is a prime reason why some people have repeatedly had their account removed, and then returned under a new user name, which, by the way, is not against the rules, unlike being banned. Even when a person is banned, their post history is still searchable.
People can conduct searches in another way than the one you have shown, too. So even if you were to make your profile private or viewable only by friends, people could search out posts you made.