Why are twisted pair cables used in electric power distribution systems?
After nearly 2 years, I found the answer to my question.

I recently walked past an electric utility's storage yard and noticed this reel of twisted pair cable.
 

The manufacturer is Southwire Company of Carrollton, Georgia and the cable is called VR2, Vibration Resistant Cable.

Their web page says VR2 uses a twist to provide resistance to Aeolian vibration and ice galloping.

Since I had never heard of Aeolian vibration, here is a quote from this article titled: "Aeolian Vibration Basics" en-ml-1007-4aeolianvibook-1.pdf

When a smooth stream of air passes across a cylindrical shape, such as a conductor or OHSW, vortices (eddies) are formed on the leeward side (back side). These vortices alternate from the top and bottom surfaces, and create alternating pressures that tend to produce movement at right angles to the direction of the air flow. This is the mechanism that causes aeolian vibration.

Here is an example of an Aeolian Vibration Failure.


Here is a YouTube clip showing these vibrations.