The ancient sources do not specify which specific miseries flew out of Pandora’s box, but I would suggest they came in three groups.
Some forms of suffering happen to human beings because of the kinds of creatures we are. We can postpone death, aging, disease, pain, and fear, but they are inevitable. These are the natural woes. Our very existence requires the death of other people, or else the earth would be too crowded for the living.
Injustices are miseries for which we rightly blame our fellow human beings. What counts as an injustice (as opposed to a natural phenomenon), is a matter of dispute. I would include sins of omission, such as my own failure to help people even though I own superfluous resources. I would include both unjust actions and inequitable states of affairs. Those are controversial claims, but no one doubts that some kinds of injustice exist.
The third category, unhappiness, is a failure to flourish, thrive, enjoy, and achieve equanimity or satisfaction.
These three categories of woe are empirically related. For example, even though death is inevitable, injustice causes millions to die early. It is difficult to be happy if one is suffering from disease and pain, or if one is a victim.
Yet the connections are loose, not logical or inevitable. In a wealthy suburban subdivision where injustice is absent and natural afflictions are normally remote, people may still be miserable to the point of suicide. In a poor village under a repressive government, people may be happier.
Even if injustice does not necessitate unhappiness, it is still an evil, not to be excused. But unhappiness is evidently a separate problem.
We pay far more attention to mitigating or postponing natural afflictions than to fighting injustice–and even less to unhappiness. Also, European and American philosophy since 1800 has much more to say about injustice than about unhappiness.
A just society harnesses science to reduce suffering. Science is also beginning to give attention to positive states of mind, like flourishing and equanimity. That opens the possibility that we could develop new methods of enhancing happiness. But if freedom is also valuable, or is a component or aspect of happiness, then the idea of engineering happiness is disturbing.
Politics is a tool for mitigating natural afflictions and preventing injustice. In liberal democracies, happiness is not seen as a political objective. A government cannot make people happy and may threaten their freedom if it tries.
Some authors (Nietzsche, Emerson) have said something like this: My duty is limited to avoiding injustice. I cannot make other people happy. At best, I can contribute to the happiness of children or partners in intimate relationships. Thus I should concern myself with achieving equanimity for myself and perhaps serve as a model for others.
I can’t accept that such a high degree of self-involvement is either ethically acceptable or compatible with happiness, properly understood. So then the question becomes how to achieve happiness while helping other people to be happy without abridging their freedom.