I think that if they would, that would be very surprising and indicative of a lot of wastefulness inside the model architecture. All these tests are simple single prompt experiments, so the LLM's get no chance to reason about their responses. They're just system 1 thinking, the equivalent of putting a gun to someone's head and asking them to solve a large division in 2 seconds.

I bet a lot of these experiments would already solvable by putting the LLM in a simple loop with some helper prompts that make it restructure and validate its answers, form theories and get to explore multiple lines of thought.

If an LLM would be able to do that in a single prompt, without a loop (so the LLM always answers in a predictable amount of time), then it would mean its entire reasoning structure is repeated horizontally through the layers of its architecture. That would be both limiting (i.e. limit the depth of the reasoning to the width of the network) and very expensive to train.