but trees and roofs don’t really go together

It's fine if they are far enough to not hit your roof, or if they are short trees. Many types of short and kinda wide trees are actually the best for shade etc. At worst you may have to trim some branches every few years.

Grass is one of the most common plant types on earth. It naturally covers vast expanses

Most places don't naturally have the kind of grass growth people want in lawns. Some places do, mainly very humid and slightly cold countries. Otherwise, while there may be grass, it's either brownish long grass or very patchy. So people waste a bunch of water on it, and sometimes pesticides too. Then there's also another issue, which is that it doesn't leave enough shelter for insects, because people try to keep their lawns clear and without weeds/bushes/etc.

Apparently about a third of all public water in the US is used to water grass. And the US actually does have places where you don't need to water grass that much, in most places in the world clear green lawns are just a waste and a shame. And idk why people don't just use clover which has many of the same issues, but is usually more resilient and looks better.