I understand that God might let human-caused evil occur because he wanted humans to have free will, but why would God let natural harms occur?

This is a very common objection raised against those that believe in God. But, they have a number of responses, some better than others. Firstly, we might think that those kinds of harms are necessary for some of the greatest virtues to be displayed. For example, we might need bad things to happen in order to show sympathy, courage, bravery, indignation etc. Many of the people revered throughout history have overcome grave injustices and that is part of the reason they are so admired. It might be added that for those that do suffer, though it is terrible on earth, they will have an eternity in heaven, thus the harm they suffer on earth is negligible in comparison. The objector might press on further: "I can grant what you say in some cases, but what about the deer that burns to death in a forest fire that we never find out about. How can that promote virtuous responses?" A weak response would be that because we never find out, i.e. we don't know it has happened, it may not have happened. It's weak because the objector has stated that it has in fact happened, our knowledge thereof is irrelevant to the suffering caused. Another weak response would be to revert to something like Descartes' position on animals, where they are mere automatons dressed up. Being automatons, the indication might be that they can't really suffer. It is weak because we can easily just change the example and swap a human being for the deer. Finally, we might retreat to the last line of defence in such matters (one that Descartes himself falls back to). That is to say that yes it seems inexplicable to us how such a thing can promote the most good, but we are in a state of ignorance compared to God's omniscience. We may not know his plan. We may not be capable of comprehending it. But that does not mean that it does promote goodness in the way the objector assumes God must. One other thinker to consider briefly might be Leibniz. Leibniz thought that the world we live in must be the best possible world if God created it. But he thought this didn't merely mean the world that had the least suffering in it. He thought that the best possible world would also take into consideration the simplicity of the world's laws of nature. He thought that efficiency in this sense was a sign of perfection. If Leibniz is right, then the best possible world may not be the one with the least suffering.