You are assuming that the primary purpose of religion is to explain those phenomena which the natural sciences seek to explain – an assumption many reject.
I think your emphasis on evolution in particular shows a particular bias – someone whose idea of religion is centered on 20th century American Fundamentalist Protestantism. Many religious thinkers have absolutely no problem with evolution. Some have even tried to co-opt it – e.g. the French Jesuit Pierre Teilhard de Chardin, who not only made evolution the centrepiece of his theology, he also was a practising palaeontologist and geologist, who made genuine contributions to the field – he was part of the team excavating the "Peking Man" site near Beijing in the 1920s and 1930s, and discovered there a species of extinct buffalo named after him (Bubalus teilhardi). So he had absolutely no problem with the theory of Darwinian evolution.
Naively it seems like that has changed. We are far less likely to believe in the power of prayer or that god is the proximate cause of events. I don't think that science is the only cause of this change and in fact religion has been a moderating influence sometimes. But science and evolution do seem particularly powerful. It does give an explanation for many of the most important events and feelings in our lives.
But i think we often take those scientific ideas for granted in the modern world. We teach kids to wash their hands and brush their teeth long before they know the lords prayer. So we don't need to look to god for an explanation of why they died of an abscess or dehydration after diarrhea. And if they do die the questions will be narrower. A question of faith more than practical cause and effect.
For many mediaeval philosophers, the primary thing God explained is "why does anything exist at all?" The existence of particular things had natural explanations, which could be studied by natural science – of course, much more primitive in those days, but they would not have had a problem with the latter developments in that field, just as contemporary philosophers who follow them don't either. Whereas, "why does anything exist at all?" is not a question that currently natural science has any consensus explanation for. Yes, it all starts with the Big Bang–but why the Big Bang? Did that happen for some known (or knowable) reason, an unknown reason, an unknowable reason, or no reason at all? At the ultra-speculative fringes of theoretical physics you will find attempts to answer it – e.g. Max Tegmark's ultimate ensemble theory – but that is far from being an established scientific consensus, and many question if it is really science at all, as opposed to philosophy masquerading as physics.
Another thing God explained for the mediaevals is "what is the ultimate source of rationality and ethics?" And those are questions for which I'd argue the natural sciences still don't have established answers, and quite possibly never will have established answers.
> Naively it seems like that has changed
I think there has been less change than you think there has been. Most people today have an overly simplistic model of what educated people one thousand or two thousand years ago believed. One encounters many people who anachronistically assume that mediaeval and ancient Christians had a similar worldview to 20th century American young earth creationists. Even before Christianity, Plato and Aristotle were much closer to today's "sophisticated theology" than the kind of "explanation for why a birds song is beautiful" you are talking about
