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.

In a remote hack or an evil maid attack, sure. If you get targeted for something, and your computer is confiscated and searched, the less ammunition stored there the better. With a large enough dataset (emails, web history, etc.) it’s pretty easy to cherry pick data points to build a narrative.

I don’t bother with this level of defensiveness but I can follow the reasoning.