For a small model (think handwriting recognition, say, 6x8 pixels), it is actually possible to construct a formal proof that the model will correctly identify digits and characters correctly. However, it is usually more expedient just to test with a large sample of typical inputs. In such cases, an error ratio smaller than what a human would produce, and the low risk of failure makes this approach acceptable.
However, for LLMs and models of the size typically used in self driving, it is practically impossible to verify the model (think heat death of the universe) using formal methods. The best that one can do is identify the desired outcome and perform statistical tests to determine the error percentage. When it comes to applications such as criminal sentencing, self driving, and applicant selection where mistakes expose the model user to substantial liability, AI may be more appropriate in an assistive role where a human must be in the decision loop. Even so, there are yet a large number of AI applications where mediocre performance (i.e. good enough, with occasional errors) is in fact good enough to justify the cost savings.
It is programs like the one proposed here which represent a structural danger to society: because of doctrines like sovereign immunity, a state which certifies a model as "safe" does not actually have any responsibility for the harm caused by such a representation. That is, a company which relies on the state's safety certification can avoid liability for harm caused by the model, and the state has neither the responsibility nor the incentive to test the model in an intellectually honest and formally rigorous way. Thus, the cost of testing the model is borne by the state, the liability for mistakes is borne by the public at large, and the disproportionate profit such an arrangement facilitates accrues to the benefit of private corporations.