Newborns of wild animals raised in captivity cannot be released back to the wild, because they lack the survival skills they could otherwise have learnt from their parents. It is true with many species - a species' accumulated and inherited knowledge, passed down generation to generation, about how to survive and thrive in the environment, is part of that species' evolution history. This apply to humans as well as to almost all other animals. It is misguided to think human evolution is "not in the hands of nature", because the accumulated inherited knowledge we have about the world, the capital we build that is passed down to our children, and technology we implement, are part and parcel of nature itself. Are our bodies nature? Are our gut bacteria nature? Do our neurons work apart from nature? Is the tendency to want to be "better than the joneses" to attract a better mate ourselves, or help our children to do so, part of nature, or an artificial phenomenon? What about our desires to live in shelter of our construction, impulse to educate our children, to pass them what we have and improve their ability to thrive? I think all of these behaviours are nature in and of itself, and because all things we do spring from nature, those things are nature too, even down to our computers and any AI we may build in the future - because products of nature is nature itself.
Nature, in the broadest sense, is the natural, physical, or material world or universe [1] If humans are separate from the universe, then where does the universe end, and we begin?
However, besides this nitpick, I agree with all your points. In the future, nature will select some genes based on their fitness as predicted by nature, as well as actual fitness at the current moment.