Professional baseball fields do just that...very green and short cut.
Of course, they have professional care and cut three times per week. Top-quality golf clubs do about the same. Top-quality grasses that are naturally dark green and will tolerate short cut, will do fine.
And yes, longer leaf blades will transpire more water.
And yes, high soil temperatures result in shorter roots. Likewise low oxygen levels--and high levels of carbon dioxide in the soil both damage roots. You need water, but do not flood the soil as that will force the air out of the soil.