I see LLM inference as sampling from a distribution. Multiple details go into that sampling - everything from parameters like temperature to numerical imprecision to batch mixing effects as well as the next-token-selection approach (always pick max, sample from the posterior distribution, etc). But ultimately, if it was truly important to get stable outputs, everything I listed above can be engineered (temp=0, very good numerical control, not batching, and always picking the max probability next token).
dekhn from a decade ago cared a lot about stable outputs. dekhn today thinks sampling from a distribution is a far more practical approach for nearly all use cases. I could see it mattering when the false negative rate of a medical diagnostic exceeded a reasonable threshold.