> that the straightforward definition of “purpose” is correct here.
That was already very clear. But you clearly don't have any better suggestion.
For example, we make a system of speed limits to make roads safer, and we have a law enforcement system. We notice later that the roads are not safer, but that the police are vigorously enforcing the law and collecting the ticket profits from doing so. We ask: why does this system exist? What is the purpose of it? The naive answer is to make roads safer to drive on. The witty, savvy, cynical answer is: …
Ie the reason the system still exists in the way it does is because its real “purpose” is to be a revenue generating scheme for the police, regardless of the intent of whoever set it up in the first place, if indeed anyone did.
If it was just trying to generate revenue for the police, it would be better at it.
Ditto, if it were just trying to make roads safer, or if its main objective was full compliance. (Which are related objectives, but not the same thing).
The reality is that political pressures exist which means neither full compliance nor the engineering interventions to make roads much safer are palatable to US voters, but there are pressures in the other direction which demand something must be done. Which is how we end up where we are.
I am not going to do it justice, but the bottom line is that systems get complex very very fast (n! factorial complexity). Cyberniticians (or Stafford Beer at least) reason that we should just treat these systems as black boxes (and examine their inputs / outputs) as any attempt to explain or rationalize the inner working of the system itself (as you are trying to do) will never go well (again because of the complexity).