As I understand it, most libertarianism don't care as much about government inspections as about not wanting the government to tell them or restrict what they might want to do. Like if they want to smoke/drink poison, why not, it's their right to kill themselves if they wish by any means. And companies are entitled to do whatever they wished. If they want to put out poisonous soda, why not, the free market will just not buy them.
I think this system was how free market was initially structured when this excellent economic concept was first invented. However, over the years, many companies that produce poison laced junk surfaced and a few incidents made the buying public very nervous. E Coli laced milk, lead polluted products etc. No one wanted to be the 'tester' of products anymore. And this fear of unsafe products shook the market confidence and reduced public buying power. This lead to a slow down of economy. People wanted to get it right, get it safe the first time around. That demand on the government lead to the creation of inspection agencies for food/medicine/architectures/plumbing etc.
I think in a word, the free market system has some bugs or flaws, the inspection agencies was made to patch those imperfections of this system or rather enhance it. The theory of free market is too idealistic and practical to be implemented in its pure form. Like many excellent theory, the practical implementation always need some tweaking.