In the sense it is intended, it is entirely correct. It is not a claim about what the intent of the people involved in the system is, it is a recognition that (1) intent doesn't really aggregate, and, more importantly, even if it did (2) intent that consistently fails, because of the nature of the system, to materialize into function doesn't matter.

It's an elegant idea in it's simplicity, but there's zero reason to think this heuristic is more valid than any other, and in my personal experience this line of thinking is usually wrong.

It's the opposite; it's a heuristic for directing thought down useful pathways and escaping a rabbit hole of speculation on matters which makes no material difference, and which largely (for the kinds of systems it concerns) also involve pointless metaphysical wankery on the order of debating how many angels can dance on the head of the pin, because the kinds of systems it concerns (which are almost all real systems that matter) aren't guided by unitary intent, and pretty much any intent you want to appply probably can be found in some subset (and, conversely, also opposed by some subset) of the contributors to the system.

A more precise statement might be "'Purpose' is not a meaningful attribute of complex systems," but POSIWID works.

The "purpose" of capitalism is to "destroy the ecology of earth by being good at organizing stuff into metastasizing accumulation strategies"?

People don't like that at all, because it's simply pretentious to reduce any system to however you choose to smugly describe "what it does".