God could have prevented or mitigated the Holocaust, but He didn't. God could prevent most or even all abortions, but He doesn't. Why?
From an orthodox Christian perspective, I would agree that God can prevent most or all abortions, could have mitigated the Holcaust, and could have prevented many other acts of evil in the world....without trampling upon free will. After all, there are plenty of examples in the Gospels with Jesus healing ailments, disabilities, and even bringing people back from the dead.
And, in view of this, you pose a question that has been brought up by students in every theology class that I have ever taught. If God can prevent these things, why didn't he?
Many Christians scholars have sought to answer this question. To a degree, their answers align with the primary source of Truth in Christondom, divine revelation in the form of the Christian and Hebrew Scriptures. However, I have yet to find (or at least fully understand) these explanations apart from revelation...I do not see them as firm logical stand-alone proofs.
Even C.S. Lewis, after addressing this question in The Problem of Pain, later wrote what I consider to be his greatest work, A Grief Observed. It is a troubling, painful journaling amid the loss of his wife. It virtualy abandons his logical appraoch in the former book and dives deep into the very personal experience of grief and human suffering.
I place the answer to the "why" question amid the mystery of God. As troublesome or apalling as it may be to some outside of Christondom, the Scriptures do indeed call for trust in and reliance upon God even when there is no known (to the individual at a given moment) rational explanation for something like this. There is a "because I said so" dynamic to the Christian faith that can't be avaoided or hidden if one is to be consistent with the Scriptures. I am convinced that Scriptural Christianity is a faith first, understand second perspecitve of life (e.g. "Faith seeking understanding.").
For the Christian, I am convinced that the most important answers to the big "why" question that you pose are existential more than logical, highly personal (although oftentimes transferable), and closely connected the human struggle with life as suffering.
My answers to the "why" question are the ones that allow me make sense of life in a messy and uncertain world. Others Christians require very different answers. While there are a number of fundamental doctrinces in Christianity, the answer to this question is not (well not directly) one of these fundamental doctrines. We are given some doctrinal paramenters, but within those parameters there is much room for a variety of individual narratives that people use to work through questions of suffering, grief, and injustice in the world.
Most of these answers can be logically attacked or rejected as easilty as one can logically critique a parent's words of comfort to a grieving child. From a Christian perspective, the answer must align with bibilical revelation, but that answer could take a variety of forms:
The child: "Why father?!"
The Father: "Shhhhh. It is ok. I love you. No matter what happens, know and trust that."
OR "Even when it does not appear to be so, know that I remain in control and that I have not rejected the world."
OR "As impossible as it may be for you to grasp, all suffering on earth is but a moment." OR "You can't understand the answer to this, but I call upon you to fight against this evil until your last dying breath. That is your charge."
OR....add a thousand other possibilities.