According to Socrates the greatest goods and evils are moral ones. Call this the "Socratic thesis". On the Socratic thesis, the worst thing that can befall one is to act culpably wrongly. Now, we may divide up the evils of the world into three classes:
- Culpable wrongdoings.
- Harms other than culpable wrongdoings resulting from culpable wrongdoings.
- Harms not resulting from culpable wrongdoings.
Each of these three classes of evils is very large. I think we can say that if we confine ourselves to evils happening to humans (bracketing the problems of animal suffering and angelic fall): Class 1 is roughly as large as the Class 2 (granted, some culpable wrongdoings result in many harms; but many culpable wrongdoings stay at the level of an evil thought that leads to no harmful action) and also roughly at least as large as Class 3. So roughly, about a third of the evils of the world are in Class 1.
Next notice that we have a theodicy for Class 1 evils: the free will theodicy, in its different versions (straight free will theodicy, soul-building, autonomy, need for love to be a free response, etc.) By the Socratic thesis, we thus have a theodicy for the greatest evils that occur, and these evils are roughly a third of all the evils that occur to humans. This provides us with some inductive reason to think that there is a theodicy for the rest of the evils: if a theodicy can be found for the greatest evils, and indeed for about a third of the evils happening to humans, then the existence of a theodicy for the rest seems more plausible.
Moreover, some versions of the theodicy for Class 1 evils extend to theodicies for many Class 2 evils. First, our free will would be a bit of a sham if it wasn't effective—if evil choices never resulted in in the chosen state of affairs. (This is less plausible for the worst Class 2 evils.) Second, while terribly harms do befall undeserving people, most of the evils that befall are, I suspect, quite deserved. Those evils, then have a justice theodicy, given a freedom theodicy for the actions that deserved them. (This might shift our count of some evils from Class 3 to Class 2, though we might also say that there are evils in Class 3 that do not result from our culpable wrongdoings, but that on account of our culpable wrongdoings weren't prevented by God.)