It could be retconned, but it at least gives the model the chance to use the space to work out a solution in smaller, easier parts.

If you ask for an answer first and then ask for an explanation after, you will most likely get self-justifying BS for an answer. You have to ask for the explanation first.

Yeah, I can easily buy that it makes it easier to learn a process. Just maybe not the one that the upstream LLM actually used.

All the LLM is doing is generating text. Forcing it to describe a step-by-step reasoning process is the only way to get it to work through one. And the whole point of using this as a prompting strategy is that it often gets you something different and better than what you might call the "first guess" it gives you if you don't ask for intermediate results.