Not entirely. Since generation is auto regressive, the next token depends on the previous tokens. Whatever analysis and decisions it has spit out will influence what it will do next. This tends to cause it to be self reinforcing.

But it's also chaotic. Small changes in input or token choices can give wildly different outcomes, particularly if the sampling distributions are fairly flat (no one right answer). So restarting the generation with a slightly different input, such as a different random seed (or in OP's case, a different temperature) can give wildly different outcomes.

If you try this, you'll see some examples of it vehemently arguing it is right and others equally arguing it is wrong. This is why LLM as judge is so poor by itself, bit also why multiple generations like used in self-consistency can be quite useful at evaluating variance and therefore uncertainty.

Yes, but I guess the model is optimized for relatively quick response, whereas these techniques are allowing the model to spend more time to generate a higher quality response

To an extent, but different models are better at different things.

That is something I'm also curious about. Given models (that use the same tokenisation) that are better at different things, would their be interesting things to find by analysing the logprobs for tokens generated from identical inputs (including cross feeding the generated token from one to another)

Surely there must be something notable at particular points when a model goes off on the wrong path.