1. We must ignore the intentions of the designers (your claim), and instead see what the outcomes are
2. Therefore we should ignore Beer's intentions when designing the phrase POSWID, and instead see how it is used.
3. The overwhelming majority of people using it on the internet (including the GP comment) is to imply that the people perpetuating the system actually desire the outcome.
So the purpose of POSWID is clearly to imply intent.
That's not "true" in any demonstrable sense, but it can be a useful form of analysis. As it is with "purpose of a system"
Also worth remembering that most systems POSIWID is said about, and in fact ~all important systems affecting people, are not designed in the first place. Market forces, social, political, even organizational dynamics, are not designed top-down, they're emergent, and bottom-up wishes and intentions do not necessarily carry over to the system at large.
IMHO the saying is meant to make you reflect.