I'm a product manager, and a lot of the things I see people do wrong is because they don't have any product management experience. It takes quite a bit of work to develop a really good theory of what should be in your functional spec. Edge cases come up all the time in real software engineering, and often handling all those cases is spread across multiple engineers. A good product manager has a view of all of it, expects many of those issues from the agent, and plans for coaching it through them.