alt Hacker News> not [...] how they should work
So that we're on the same page, what I think should be PM responsibilities:
If I have a user story: "As a customer I want to purchase a product so that I can receive it at my address" - PM defines this user story as they have insight to decide if such feature is needed.
PM should then define acceptance criteria: "Given customer is logged in When they view Product page Then 'Add product to basket' button should appear", "Given 'Add product to basket' button When customers click on it Then Product information modal should appear" etc - PM should know what users actually want, ie whether modals should appears, or not; whether this feature should be available for logged users only, or not.
How this will work shouldn't matter to PM; these are AC they've defined.
Of course the process of defining AC should involve developers (and QA), because AC should be exhaustive to delivering given feature
The problem, in my experience, is that most PMs don't add anything when it comes to drawing up the acceptance criteria.
In your example of an order placement - the PM has no special knowledge of what is a good customer order flow. Developers are usually way better at coming up with those by the dint of experience and technical knowledge of the current codebase and make the appropriate speed/polish trade-off.
PMs acts as an imperfect proxy for what the customer wants, making judgements off nothing more than their own taste. And though there are many great PMs, the taste of a PM is usually worse than that of developers and designers on average.
IMO the main business reason they exist is for organization accountability and ownership, despite the often negative value they bring.