Atheists and naturalists are always trying to get something for nothing, so they are always looking for some silver bullet argument that will make it unnecessary for them to get into the messy details. By far the most popular candidate in this regard is the claim that a miracle, or Christian theism, or a miraculous Christian theism, is just "too improbable" at the outset to be bothered with. In this category we can place Hume's claim in his essay on miracles to have delivered an "everlasting check to all kinds of superstitious delusion."
A more sophisticated recent version of this is the claim that Christian theism or even classical theism is so complex an hypothesis that it has a very large burden of proof--worrisomely and discouragingly large.
In this context there is a further fear that, in responding to the problem of evil (POE) by including the idea of a fall of man, chosen evil, Satan, or even just the general notion that God intended things to be perfect but that they were marred by the choices of finite beings, we have saddled ourselves with an ontologically complex hypothesis. The idea there is that such an ontologically complex is therefore a worse explanation of the data than some allegedly more modest naturalistic hypothesis. (E.g. Suffering is a result of evolutionary chance; nature and man were not created by a good God.)
The claim that Christian theism is worrisomely complex needs to be met with the philosophical principle of "no double standards."
How does the "no double standards" principle apply? Ask yourself how many complex things you believe today in non-religious areas. For example, you believe that your mother exists, and presumably you believe a lot of things about her. Nobody had to convince you that your mother's existence had a "high prior probability" before taking into account the specific evidence you have for her existence (e.g., your memories of all the things that she has done for you). That would be ridiculous. We never approach everyday affairs by asking what the probability of an hypothesis would be if we had absolutely no evidence for it!
This is not to say that simplicity considerations have no role to play. They do. But their role should be comparative. For example, suppose that we ask how you could account for the evidence on the hypothesis that your mother does not exist. You would have to bring in some sort of massive memory creation on the part of your subconscious mind or on the part of some Cartesian Deceiver or mind-maipulator. Or perhaps you would have to hypothesize that what you call "my mother" is really an android, a space alien, or a holograph that has been cleverly designed to look like a human woman and to act like a mother to you. Now all of these are obviously much more complex hypotheses than the hypothesis that your mother really exists.
So complexity and simplicity considerations come into play in considering a) the evidence at hand and b) various alternative hypotheses for explaining the evidence.
Virtually everything we believe on a day-to-day basis is very complex, when we consider its details: For example, that giraffes exist, that the Civil War occurred, and that Barack Obama is presently the President of the U.S. If you were to spell out for each of these what you mean by "giraffes," "the Civil War," or "Barack Obama," you'd come up with a lot of complexity in the detail. That isn't a problem, though, because the evidence itself requires relatively complex hypotheses.
The same is true of Christian theism. We have a large variety of evidence and must explain it, and the evidentialist apologist says that Christian theism is the best explanation of the evidence at hand. At that point it is a sheer head-fake to try to take us back to a pre-evidential situation and get us to worry about what the situation would be like if we had no evidence!
If anything, we can note that even in the absence of all the complex empirical evidence, we would still have various a priori arguments of natural theology, which is more than one can say for everyday beliefs. If you had no empirical evidence for your mother's existence, you couldn't argue in a purely a priori that a Generic Mother must exist as the First Cause. So in that sense, theism has a leg up on everyday empirical propositions.
Be that as it may, we of course want to argue for something more than generic theism or even generic classical theism. We want to argue for Christian theism, specifically. And that is where the evidence of revelation and miracles comes into play and must be accounted for.
At this point, though, I want to go back to the question about the POE and the alleged complexity of answers involving evil choices, evil beings, and the like. This question lies somewhere in the uneasy middle ground between pure natural theological arguments (such as the moral argument) about the existence of a generically good God and full-bore historical arguments involving the special, revelatory acts of God such as the argument for the resurrection.
Are we who believe in a good God forced into a somewhat uncomfortable position of having to hypothesize a complex hypothesis to account for suffering and evil while the atheist has no such burden? At that point do we simply say that the further evidence for Christianity is so strong that it can overcome this previous disconfirmation by suffering and evil?
I don't think so. Here is why: When we consider evils such as pain and suffering, we need to consider a wider array of evidence that includes natural goods as well as evils. Presumably the person raising this objection is not permitted to say that our feeling that there is "something bad" about the pain of cancer is "merely subjective." If one could dismiss our sense of axiological badness ("problem of suffering," "problem of pain," dysteleology, etc.) that easily, then the atheist would have no data to use in this argument, because by his own account this "sense of badness" would have no meaning. In which case, how could he argue that a good God would not permit such evils?
But in that case, another part of the data at this same level is all of the axiological goodness in nature. We could instance the tenderness of many types of animal mothers, the incredible ingenuity in evidence in the mammalian immune system and its ability to fight off disease, and the beauty of a butterfly. This is partly a matter of the argument from design, but it goes beyond that to the axiological goodness of design. Just as there is something ugly (or so it seems) about "nature red in tooth and claw," there is also something valuable about the marvelous adequation of means to ends in creatures.
When we come to human life, this combination of glory and horror is especially striking. The atheist instances human suffering, such as severe psychological illness or the pain of watching a loved one die slowly (not to mention the pain of the loved one). It is fair to say that there are distinctive ways in which rational creatures can suffer beyond the ways in which non-rational creatures can suffer. Does the existence of all of this suffering disconfirm the idea that God is good? Perhaps it would if it were taken all by itself. But we should consider a great deal more evidence available even aside from the specific evidence of divine revelation. Consider, for example, the many natural goods that are unique to humans: The ability to create and enjoy artistic masterpieces in a wide variety of media, the intense joy of contemplating beauty, the availability of beauty for man to contemplate, the glory of human romantic love, the pleasure and goodness of love between parents and children, and so forth.
What does all of this mean? I think it means that we are (even before taking into account the specific evidence for Christian revelation) in precisely the sort of situation in which the evidence itself is complex. We have evidence of both good and bad things, beauty and ugliness, glory and horror, intense suffering and intense happiness, in nature, including human life. Hence it follows pretty much necessarily that an adequate explanation will also be complex.
Notice that a truly naturalistic explanation would "explain away" rather than explaining. Naturalism has no room for axiology. It is meaningless to say that the pain of cancer is "an evil." It's just something that happens. There is nothing particularly bad about cancer, on naturalism, any more than there is something particularly good about human love or artistic genius.
So naturalism is a non-starter as an explanation if we are to take the problem of suffering seriously in the first place.
The evidence, therefore, leads quite naturally to some notion that "things were meant to be one way but something went wrong," etc. A sort of "poor man's Manicheean dualism" would be a rather understandable direction to go if one had no evidence from special revelation, unless one were able to argue philosophically for the conclusion that evil is a privation. But aside from that philosophical question, the point is that the evidence itself forces us to hypothesize something much like the Judeo-Christian idea that something originally good has been marred, that there is a conflict (in some sense) between good and evil, that there are causes at work that have brought about both genuinely good, valuable outcomes and genuinely tragic and undesirable outcomes.
Hence, in relation to the whole set of evidence regarding goods and evils, suffering, beauty, and joy, a theodicy involving a being like Satan, a human fall, conflict, etc., is not problematically complex relative to any other hypothesis that has a similar hope of explaining the complexity of the evidence itself.
What the problem of evil greatly disconfirms is a kind of Generic Pollyanna Theism according to which not only is God good, but that is all that there is to be said about the matter. But almost nobody (except maybe Joel Osteen followers) believes Pollyanna Theism, just as almost nobody believes in a Simple Mother, because of the complexity of the evidence itself.
If you are a non-theist, you're also going to have some 'splainin' to do, because Simple Atheism will be of very little help relative to the richness of the evidence of goodness and badness in nature.
Simplicity is indeed a theoretical virtue. But it does not even begin to follow that we should believe in a simple world. That would be simple-minded.