My intuition is that AI agents are, at this time, bad at product management, because they have a strong bias toward following instructions.
I've let an agent design the interface of a command line tool. The agent added a lot of features that made the tool worse. It did this because, when it sought feedback from other agents, the agents said, "It needs to do X" and "It would be nice if it did Y", and the result was a clunky, inefficient UI.
A better agent would have pushed harder to see if the requestor's need could have been fulfilled easily with the existing tool.