The roots don't move per se, but they don't exactly stay put either. Grass loses significant root mass in summer, stores energy in new roots in fall, and uses that energy to get going after winter. The plant is constantly depleting or recharging its root system, so it never grows out of the need for some deep soaking waterings.

It's kinda like having a person work out really hard and get huge biceps. What happens if they stop working out? They slowly lose muscle tone because they aren't replacing what nature slowly destroys.

Adjust Irrigation Frequency, Not Amount of Water Applied

The amount of water applied at each irrigation event should remain consistent. Your objective should be to train the roots to grow as deeply as possible. If turf receives frequent, shallow irrigations, the roots will happily stay in the top few inches of soil, but if water is applied for longer periods, roots will seek the water out at the deeper soil levels. Deep roots can generally be achieved by applying 3/4 to 1 inches of water each time you irrigate. Never irrigate to the point where you have surface runoff of applied water. This is the point at which water is being wasted and is not benefiting the plant.