For instance, you might think that if you point out an outcome that everyone seems to agree the educational system should achieve, and then point out that this outcome isn't being achieved at all effectively, then people in charge will wake up to that fact and this will be enough to effect change in the system.

This is not what I expected when you mentioned the Just World fallacy. If you notice an outcome that everyone seems to agree the educational system should achieve, and notice that it is not being achieved at all effectively, that may be because there is no practical way to do so. Now that's an unjust world.