That's stupid. How many people are arrested and not tried or found not guilty of a crime in the US. With this you have an end around where you don't even have to nail someone with an initial crime. Just deleting browser history. If you don't think something like that could happen, see what the IRS, ATF and OSHA did someone who was trying to start a PAC.
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.