I'm trying to wrap my head around this . . .
It makes more sense to me that the hotter the water, the more cold water you would add to your shower, thus giving you a longer shower run.
John,
Think of it this way. The water is 130 (F) coming out of the hot water line. Let's assume the cold water is 60 (F).
Depending on how you mix the hot and cold water, the temperature coming out of the shower could be 130 (F), or it could be 60 (F). If you mix the hot and cold equally, the temp of the shower will be 95. That's just a bit cooler than your body temp of 98.6.
If you want a hotter shower, you change the mix to 60% hot / 40% cold and the temp of the shower might go up to 100. If you want it really hot, maybe you mix 75% hot / 25% cold and it goes to 108.
Now if you start this exercise with hot and cold faucets wide open, and change the mix by reducing the cold, the run time won't be affected, but water flow will decrease. But if you start with the faucets 60% wide open and change the mix by increasing the hot and decreasing the cold, you'll use more hot water for any given period of time while maintaining water flow.
If you have good water flow, you may be starting with the faucets less than wide open. If you have poor water flow, they'll probably be wide open.
So there are several factors involved, but what we're talking about is the volume of hot water from the tank that comes out of the shower head for a given length of time. Hotter showers often take more hot water.