> LLMs collapse and start outputting garbage after a number of tokens if you do not sample and just pick the "best token" each time.

LLMs are likely to get stuck even with sampling if asked to generate tokens on their own long enough, though sampling does tend to stretch out the time before that happens (as do other techniques that don't involve sampling, like applying repetition penalties directly to token logits). But LLMs generally aren't left to infinitely extend their own output, and the length response typically needed in the use case is much shorter than the would result in collapse given the kinds of inputs expected in that use case, the existence of the theoretical eventuality may not really matter.