Your analogy misses the point that a fallback mechanism is needed in the rare cases where something unexpected happens. Even in cases where you have everything

Your analogy misses the point that a fallback mechanism is needed in the rare cases where something unexpected happens. Even in cases where you have everything formally defined, you could still have some axiom not holding, or a transient hardware issue - a random bit flipping in memory for instance. Putting simply, everything fails eventually, the question is not "if" but "when".