> The optimal amount of crime in a society is non-zero because a society with zero crime would be a dystopian police state where innocent people sometimes get caught up in the justice system's net to make sure it catches all of the criminals.

At this point you're just playing with the definition of crime. I would argue that it is criminal to deprive an innocent person of their freedom, and challenge that your proposed scenario is actually "zero crime".

Secondly, you talk of catching "all of the criminals". In a "zero crime" environment there are no criminals - by definition if there is a criminal, then a crime has been committed at some point.

All that said I agree with your larger point - the cost of freedom is that people are not constrained before the fact from committing crime, and that's a good thing on the whole.