So your thesis is that it's silly to talk about school effectiveness because of the larger socio-economic condition of the population.
In other words, given certain external conditions, there should be no successful schools.
Proceeding down this path of analysis, you should find counter-examples, if they exist, and begin listing conditions that make schooling impossible.
Also not my point, but certainly a fun exercise. So close the schools, provide the useful public services they offer (if any), and work on the larger conditions.
The question remains whether or not the political structure that is paying for and supporting these organizations is honest enough to stop the dysfunction when it's thrust in their face. Even in your scenario, close them.
ADD: I want to point out that there is this Stupid Human Trick we all do: when presented with a situation that involves difficult-yet-implementable decisions, we point to some larger, impossible-to-solve situation and demand that this situation be addressed first. It's a way not to deal with things. I've spent decades watching Cold War arguments play out with "Well, if we had peace in the Middle East, these other things would also fall into line"
We were never getting peace in the Middle East. But it was easier just to throw their hands up and ask for the moon than it was to make the simple, immediate decision that was achievable.