Destroying evidence has been illegal for a long long time. I don’t even think it’s a new development to consider your browser history evidence. And yes they do have to have some reason to suspect you first, otherwise they’ve got no reason to think there’s evidence.
And I've been known to delete my browser history so my wife won't get the popups on her computer that tell her which gifts I'm looking at. Also being a Freeper, I investigate a lot of stories I read here and may go to some nefarious sites. If you put these two activities together I could to be guilty of a felony. With more and more people thinking like you we are close to embracing a police state.