>In my view, "show your work" means, loosely speaking, to create a fictitious chain of reasoning and present it in a style learned from the textbook and classroom presentations.

This doesn't just arise from students guessing. For any "difficult" problem, most students will end up doing useless steps, or possibly going down rabbit holes before finding the correct path. I don't think I have ever seen a proffesor that appreciated seeing all of this work (unless you couldn't find any path, in which case they often seemed to appreciate seeing what you did try).