I do actually believe that a fully libertarian society could sort out the issues of restaurant food safety and elevator safety. And, fracking safety. But many people I talk to have tremendous faith in the power of government, and only government, to keep us safe.
As opposed to your faith that the "free market" will keep us safe. That the private sector will have their own inspectors, and private inspectors will take over the role of government inspectors, and everything will be peachy.
Except it won't. Take the recent case of mortgage backed securities. All of the ratings agencies were giving these pieces of shit obscenely high ratings, up until well after it was discovered they were toxic. And why were they doing that? Because of the free market rating system. If the ratings agencies didn't give them inflated ratings, the bond holders would simply take their business to someone who would. You can see the same thing with Orange County debt and one of the ratings agencies. After Orange County declared bankruptcy, and the bonds (which were rated very high) were discharged, people sued the ratings agency. The ratings agency was found not to be liable simply because they "offer advice".
Are you honestly going to tell me that the exact same fucking thing won't happen when private inspectors take over safety? Or food?