Browser history is nothing but self incriminating evidence. Why would you keep it around?
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.
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.
I don't generally do anything "incriminating" that would need to stay out of my browser history, and even if I did, clearing your local browser history isn't going to mean much: If it's truly criminal stuff you're talking about, all the websites you use are likely subpoena-able anyway and they'll get your "history" one way or another.
For mildly "incriminating" stuff that isn't illegal, just use an Incognito window. :-)