It's the same. Dried stalks that are dry and crispy are dead, and they are dead to the plant, too. It's like your hair. Inside your skin, it was alive in the hair follicles, but now it is dead. Do you (or your body) physically care if it is cut off or not? No. We do it because of aesthetics: it looks better.
During droughts, especially, the soil heats up. This is not just because of the excessive heat, but even more because there is less foliage to shade the soil and keep the temps from baking. Anything that will shade the soil and/or slow evaporation of moisture, mulch, for instance, will be extremely beneficial.