That's a theory, but the theory does not describe reality. Reality is that human beings defraud each other frequently, and in fact that is one of the main reasons we have governments, laws, and regulations. When you buy a house or obtain a loan or some software, or walk down the street, do you assume nobody would be doing anything corrupt or fraudulant, just trusting everyone? Of course not.

Anarchy leads to chaos and conflict. Caveat emptor.

EDIT: Major edit

Safety certification businesses competing with each other will become a function of publicity above all else, who can market and present themselves in the best way over which certificate authority actually is most stringent.

Individuals generally do not have the time or skill to evaluate which safety certification meets their own values (and if in fact their own values are even sensible and rational!).

This is why it's generally better (note: not perfect) to trust this function to a government who probably will do a better job and can be more trusted of it than a for profit institution that has conflict of interest baked into their entire model.