>You don't mention that trees also regulate the local microclimate; they tend to make rain, for example.

Good point. I'm usually so eager to mention that, too!

Trees regulate not only the microclimate, but the macroclimate as well. Isotopic analysis shows that about 80% of all terrestrial rainfall is caused by transpiration from trees and other plants. Trees essentially act as a giant inland irrigation network, using solar power to transport water via the airstream to power the water cycle. https://www.nature.com/articles/nature11983

So trees cause rain. This explains why deforestation causes desertification. I would also recommend the excellent Greening the Desert documentary for an example of the reverse process. https://www.youtube.com/watch?v=2xcZS7arcgk