You are right with the analysis, but wrong with the conclusions. Yes, LLM „thinking process“ is kinda non-deterministic in a sense that it does not follow logical reasoning and will not produce logically correct results in 100% cases. It has an error margin.

However, error margins are in the center of any engineering discipline. We cannot produce things measured with 100% accuracy. This is accepted fact. The focus is always not on eliminating errors, but on reducing them to acceptable minimum. With LLMs we should not expect an ideal logical thinker, but a process that may error sometimes, and we must design quality controls instead that push LLM outputs within acceptable margins. And it can work.