He did. More still, he gave up his life for every single sufferer who had ever lived or would ever live. Possibility you have read the story of the Incarnation, the Crucifixion, and the the Resurrection? It is not only a question of why is there evil? It is also a question of
what does God do about it?
People who ask this question often have the misconception that God sits on his hands, just letting bad stuff happen and doing nothing and planning to do nothing about it. But this is really mistaken. God doesn’t sit on his hands and do nothing. Rather, he became man (the Incarnation) and shared in human suffering. He suffered hunger in the desert, rejection from his hometown, misunderstanding from his family, the attacks of demons, betrayal by one of his closest friends, the evil of a corrupt government, the evil of a corrupt religious hierarchy, and finally, the cruelest death that society could devise. In the end he cried out “my God, my God, why have you abandoned me,”- a moment when God himself looked on the suffering in the world and seemed an atheist.
And after he suffered, he rose from the dead, (The Resurrection). In some way or another (how is another discussion), his death and Resurrection opened heaven. Before, he ascended, he said “I am going to prepare a place for you,” while St. Paul speaks of Christ as the first fruits.
The English cardinal Newman once said that if he did not believe all the suffering of the world would be made right by God in the afterlife, “why, I should go mad.” But the Resurrection does give us reason to think that a next world does exist to make right the sufferings of this one.
You ask essentially ask “wouldn’t it be better to not exist than to suffer?” The problem is that you are reckoning without heaven. The sufferings of this world seem terrible now and they are, but once heaven is obtained, the sufferings will appear to be nothing compared to the joys of heaven. And God himself suffered and died to open heaven for us.
Would it be better to never exist, than to suffer and have heaven at the end of it all? I have a hard time thinking so. Many saints have decided that any earthly suffering was worth it to obtain heaven. St. Paul (who suffered rather alot himself) said “I reckon the sufferings of the present life and not to be compared to the glory that awaits us.”
I haven’t said a lot on the free will thing, though if you want I can; but I do have a hard time imagining how free will could exist without at least the possibility for evil. If people are to be free to do good, they have to be free to “not” do good. If they are free to choose God, they must be free to reject Him. And if they do reject Him, the results are terrible. But for this reason God suffered, died, and opened the doors of heaven, so that the evil in this world would not be the final answer.
Rather immodestly, I have a few scattered reflections posted on suffering and God’s action if you like.
thesparkandtheflame.blogspot.com/2011/03/god-suffering-and-earthquake.html
More usefully though, you might look at some accessible books on the question.
C.S. Lewis
The Problem of Pain
NT Wright,
Evil and the Justice of God
I have not read, but have heard recommended, Peter Kreeft,
Making Sense out of Suffering