I've been reading lots of papers recently based around 'the Argument from Evil', its replies, the theodices and their objections. I'm agnostic but have always thought that the best reason for why non-human animals and children suffer in such terrible ways is because if they didn't we wouldn't question the existence of God.
If we didn't have arguments based around a young fawn dying a slow, agonizing death in the forest then the Argument from Evil wouldn't be as effective as it is. We could come up with answers based on redemption from sin and so forth. The same can be said for AIDS, the plague, Auschwitz, whatever. The notion of mystery on the issue and freedom of thought that goes with it is in my mind one of our greatest gifts. If we didn't have these terrors then a beautiful sunset or a kind gesture or the stars would be enough to convince most of us (or at least a fair few of us) that there must be some kind of God.
This doesn't seem to be covered by any of the theodices; the closest I can...
The problem of theodicy is a marvelous one, isn't it. I can't tell you how much pleasure I've culled from it, as have my students. For myself, I can't think of anyone whose put your point in exactly this way--but I don't pretend to command the enormous literature on the subject. I think an objection, or at least a question, might be raised to your point along these lines: Why is it better that people question the existence of God than not question? Wouldn't it be better if God were simply manifest to all and that there were no good reason for doubting God's existence? What possible advantage is served by God's hiddenness that isn't overwhelmmed by the enormous loss of souls it yields? You yourself raise a second objection: there seems to be a superfluity or excess of evil even if your point is granted. Therefore, the idea that evil is justified because it makes it possible to question God's existence doesn't seem sufficient.