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.