First of all, no one is just as King David proclaimed "Behold, I was brought forth in iniquity, and in sin my mother conceived me." (Ps 51:5) St. Augustine reflecting on childhood realized that in children there was a streak of selfishness even before they could speak as he wrote, "And now little by little I realized where I was, and wished to tell my wishes to those who might satisfy them, but I could not; for my wants were within me, while they were without, and could not by any faculty of theirs enter into my soul. So I cast about limbs and voice, making the few and feeble signs I could, like, though indeed not much like, unto what I wished; and when I was not satisfied— either not being understood, or because it would have been injurious to me— I grew indignant that my elders were not subject unto me, and that those on whom I had no claim did not wait on me, and avenged myself on them by tears." (St. Augustine, Confessions, BK I, Ch. 8)

In time of war or natural disasters the good people suffer with the wicked.
Why is this so?

Here there is no simple answer because God's wisdom is inscrutable or beyond our full understanding. St. Augustine points out that no one is so good as not to yield to concupiscence some times. Further, good persons at times fail to admonish evil doers out of human respect or fearing the loss of temporal goods. Even person who dedicate their lives to God are too concerned with their good name. Finally, we love this world too much, that is, we become attached to persons and things which when taken away help us to realize that nothings lasts and that we better put our trust in God. For these reasons God allows the good to suffer with the wicked in this world. (St. Augustine, City of God, Bk I, Ch. 9)

The above does not answer the question why children without personal sins die in natural or man made disasters. It is because the evil effects of sin of the fathers are visited upon their children. We are not individuals to such an extent which shields us from the effects of the sins or mistakes of others. So a child dies in an earthquake, in a city built by his fathers on an earth's fault. His temporal death is not due to his personal sins but his integral dependence on the rest of the fallen human race. In some way fallen humanity must die regardless of how. Physical death is not the ultimate criteria of God's goodness.

"Not for vengeance did the Lord put them in the crucible to try their hearts,
nor has he done so with us.
It is by way of admonition
that he chastises those who are close to him."

(Jd 8:27)

6. Suffering of the Just One