The original phrase, "the purpose of a system is what it does", was coined as a contrast to people saying "the purpose of this system is X" even though it consistently fails to achieve X. It does not make sense to look at an arbitrary problem and declare that the system is that problem or exists to produce the problem.
I don't understand your point. Identity and effect are not the same as purpose, but identity also isn't the same as effect. If a news headline read "Bars are encouraging foreigners to drive drunk", and the contents were just that the reporter compiled a list of 14 foreigners who were served alcohol when the bartender knew they drove there, I would say that's similarly misleading.