How tall should turf grass be? Well, what do you want to end up with? Something nice to walk on? The manicured look? Easy maintenance? Minimum water usage? The best place to start is with a look at the physics of light and heat. When sunlight reaches the surface of almost any given object it is absorbed and turned into heat. Heat is a form of light (infrared) that can travel through solid matter, i.e. rocks, concrete, pavement, bricks, soil, shoestrings, soap bubbles; you name it and heat can move through it. Heat moves faster through things that are dense and slower through things that are fluffy. There are, however, instances when light is absorbed that it does not become heat.
Say for instance when light strikes a green leaf or blade of grass. What happens next is a wonder, a miracle, an event so awesomely complex that no computer yet devised can track even one second’s worth of activity taking place within a single cell of the simplest plant. What we do know however, is that instead of turning into heat the light is used via the agency of chlorophyll, to make sugars, carbohydrates, fats, and proteins which are organized into larger structures called plants. In short, light is used to drive the biological machinery of plants instead of turning into heat. The rest of us life forms who cannot do this are deeply in their debt.
If you have a lawn of green grass, light striking it is used up powering the biological reactions that grow the grass. Some of the light reaches the soil and is turned into heat. Taller grasses mean more light is used up driving biological processes and less is absorbed by the soil and turned into heat. Cooler soil means soil that holds more water. Soil that holds adequate water not only provides for the needs of the plant populations growing in it and on it (not just grass), but also becomes a hospitable habitat for a very large array of soil microbes. As mentioned earlier these air breathing microbes do the work of making nutrients available to plants. Taller grasses, cooler soil, greater water retention, and better soil ecology.