At first glance, it is an innocent measure supposedly meant to 'protect'. Even if 'nothing bad can happen' as in a falsely accused person would not become under arrest and the shops, Services and institutions would not need to hand out any of their information to the Authorities, them being denied Service would significantly lower their quality of living.
That environment sounds like it would incentivize accused criminals to face their accusers in court. What's wrong with that?
That's my exact point: A "mixing site" is just someone else's wallet. Unlike exchanges or casinos, a "mixing site" is not a service since there is no underlying purpose for the site's existence.