It exists, it's called a geothermal heat pump / ground-source heat pump.

You can also leverage the stack effect[0] with a whole house fan[1] if you have a basement. It drops my temps about 5 - 10 degrees allowing me to put off turning on the AC for a month or so a year.

[0]https://en.wikipedia.org/wiki/Stack_effect

[1]http://www.northerntool.com/shop/tool/product_200510953_2005...

That typically refers to cycling water underground and using it to immerse one side of a heat exchanger, does it not?

I am wondering why cycling air directly with no heat pump isn't used more often.

Because air is not very good at moving heat, so it's more efficient to use water or some sort of refrigerant.

In the context of a heat pump yes, but what I'm saying is why not cycle the air of a building underground directly? I would think lots of air would be moved for very little energy and could be put through an underground radiator with lots of surface area.

Even with a heat pump, air has to be passed over the evaporation coils anyway.

If you're trying to cool a building, the goal isn't moving air, it's moving heat. Pushing air around is a convenient way of moving that heat around inside a structure, but it's a lousy way of changing the total amount of heat inside the structure.

But again a heat pump is still running air over the evaporation coils so how does that end up better than having a radiator underground?

The amount of surface area you would need to have underground to expose the air to would be tremendous. The reason heat exchangers work is because they substantially concentrate the heat (or the 'cold'), reducing the surface area needed.