A Las Vegas algorithm requires that you have a deterministic test that can definitively determine the correctness of an intermediate result. So what you're saying is that what it takes to make LLMs give 100% correct results is having a human between the LLM and the user, who's capable of re-prompting on incorrect answers from the LLM. Well, if the human is there, why not just ask the human? What value is the random number generator adding?

Like the GP said, the point of determinism is that you can trust the correctness of the results, without doing any checking. Solved problems stay solved.