Cost to whom? Imagine all the lost revenue if people would have a rational basis to trust each other more. Less transactions due to more informal exchanges must mean lost revenue to someone.
To make it short : Money and time lost due this lack of trust could be allocated to more valuable endeavor, such as pretty much anything.
Therefore it is better for society to solve this issue, even if it means some specific people that were making money out of it beforehand will not be able to anymore.