You said "Had OP made ChatGPT write an ordinary program" but that assumes enough structure exists to specify that program. If so that may be the right architecture, but also demonstrates why the "agentic AI" does not automatically solve the original open ended task.

You have converted a fuzzy task into a conventional software engineering problem, and then relying on conventional software for the reliability :-)

> converted a fuzzy task into a conventional software engineering problem, and then relying on conventional software for the reliability

What can I say? This is how I get results from AI. It also gives me context & tools to fight the AI when I have to.