How is the "problem of evil" regarded as a problem at all? The claim that God is omnibenevolent is not evidential but metaphysical: He is good as a matter of necessity. Theodicy, properly understood, then, is simply an endeavor to reconcile the fact of evil with the necessity of God's omnibenevolence (a thing so necessary that even to say "God's omnibenevolence" is, strictly speaking, a redundancy). The problem of evil depends for its force on the claim that there is no possible reason why an all-good God would tolerate any evils. So it suffices to show that there is at least one possible reason why, even if we can't know for certain if it's true.
We may, for instance, suggest that the toleration of evil is instrumental: we may say God allows certain evils because they cultivate virtues such as self-sacrifice, courage, patience, or temperance, which would not exist in the absence of those evils. Or we can suggest that evil, being convertible with imperfection, is a necessary feature of any entity that is not God, who alone is perfect.
Or (and I think this is the proper response) we can simply point out that "all-good" does not mean "actualizing every possible good" any more than "all-creating" means "actualizing every possible being" (a fact pointed out by Just Thomism's James Chastek); it suffices to say that all the goods which exist are owed to God (just as all the beings which exist owe their existence to God).