They can mow every week but need to set the mower so it mows higher. Taller grass uses less water for the reasons listed above. I am the VP of our HOA and we just went through this with our landscaper. If they plan to mow every other week, you should be paying half the price. But next they will be telling you that they need to raise the sprinklers because after two weeks, the sprinklers will not clear the grass.
Landcaping companies know all the angles and will use every one.
Daisy