The interesting part of this question to me is the phrase "so much". It implies that some degree of suffering is acceptable, but Lord, why does there have to be so much of it? And why does the suffering we endure have to be so horrible?
Pondering the implications of this leads me to imagine a world in which God did not allow suffering to build to the level we endure. In this world, the worst thing that could happen would be, say, a sprained ankle.
BUT! The inhabitants of such a world, never knowing any alternative, would react to such minor inconveniences just as we do to things like genocide. Philosophers would wrestle with the seemingly insoluble problem of God's alleged goodness in the face of such hideous evil as a sprained ankle. (And it happens so often, sometimes as much as twice in a single person's lifetime! WHY, GOD, WHY???) Even if God fundamentally changed the way our world works to reduce the level of suffering, within a few generations the pains we endure now would be a distant memory and our descendants would be...well, a bunch of damn whiners by our standards.
(This train of thought gets even more interesting when you start to wonder if maybe things could be a lot worse than they are, and perhaps the reality is that God has been shielding us from unimaginable horrors all along.)
No, the only lasting solution would be for God to come down and make some real changes. Sickness, injury, and death would have to be totally eradicated. The human body and the human mind, human nature itself would have to be radically transformed. We would be left with a new world of perfect human beings living forever in peace and joy.
We find, then, that we arrive at exactly that which the Church has taught since the beginning. The knot of God's goodness, human free will, and the presence of evil in the world will be straightened out in the end. But then one could ask, why wait? God seems to be taking a long time putting all his pieces in place, and in the meantime we have to suffer. Again though, this begs the question: how do we determine what a reasonable timeline is in which God should act? A child can't understand why a thing she wants can't happen now, because she doesn't know enough yet about how things work to comprehend all that must go into producing that final outcome, and an hour spent waiting seems like an intolerable age to one so young.
The idea that God allows evil of any degree for any length of time because we have the right to choose between his way and our way, and the attendant consequences are only proof that this is a real choice, obviously fails to convince some. What I will throw out for consideration though is that this issue might not be well addressed by logical proofs because the deity in question is conceived of as a person. Anyone who has gone through a difficult romance knows that illuminating the motives within a lover's heart and mind involves other faculties than rational thought. There is even a point at which we have come to connect with that person on such an level that behavior that once baffled us can now be understood intuitively, though we may be at a loss to explain it convincingly to someone outside the relationship. We learn, to the degree that we come to know God, that he is good; and this knowledge, though it fails to satisfy those who want paradoxes like this resolved before they will take a step further, has throughout history endowed its bearers with strength to confront lynch mobs, police dogs, assassin's rifles, and every other conceivable threat in the pursuit of a good which is no longer abstract, but can be loved and defended as one loves and defends a child.