The reason I used it is that the correct answer to the actual problem is unknown and nobody has any idea how to solve it. No amount of sampling an LLM will give you a correct answer. It will give you the best known answer today, but it won't give you a correct answer. This is an example where LLMs all give correlated answers that do not solve the problem.

If you want to scale back, many programming problems are going to be like this, too. Failure points of different models are correlated as much as failure points during sampling are correlated. You only gain information from repeated trials when those trials are uncorrelated, and sampling multiple LLMs is still correlated.

the correct answer is "the solution is unknown"