What exactly is the point of this? Is there some advantage to having a cooler sink?

I think maybe the word 'sink' has apparently confused Mr. Anderson above.

I personally think this is a great idea. In summer in my area, it still gets quite cool at night. I think if I had a 'room' (not sink) full of ten tons of river rocks, I could suck this cool night-air through the rocks, and even spray water into the air to get additional evaporative cooling. The electronics would moniter the outside temp and when the outside temp start increasing, the air intake would seal and the water spray would shut off and drain. Then, later, when AC is needed, I'll circulate the air from the house through the cool river rocks and it can provide much of my cooling.

I'm pretty sure this system isn't new, because in Engineering school in 1988, I was assigned a heat-transfer problem to size how large a river-rock bin would have to be to cool a certain size building in this manner. The size-numbers were really reasonable. Our 'building' was placed in the desert, where nightime temps are considerably cool, while daytime is really hot, so it made the exercise even more reasonable.

Still, it seems like such a great idea. I don't know why its not common. Something similar could probably heat in summer or overnight in areas where it's warm in the day and cold at night. Or you could have two 'rooms' of rocks in the basement--ones that gets cold overnight and others that store heat from the day.