Browser history is nothing but self incriminating evidence. Why would you keep it around?
If authorities already have the means to access your browser history then deleting it won't accomplish anything. They can just install malware and see what you're browsing anyway.
Why? I don't really have anything that dangerous, illegal, or weird open... And the browser history on my local machine is at most exposed to me and my fiancé, who I don't really care to hide it away from.