I came across a video demonstrating that how dogs drink water is not what you might assume. A dog's tongue is more flexible than a human's and can curl back on itself to scoop water out of the bowl rather than lapping it like ice cream.
This video answered the question of why Sugar, my dog, always left a half-inch of water in the bowl: there wasn't enough room to scoop water. The water in the bowl made it hard to tell when Sugar needed more.
But by wedging the bowl, the same amount of water is given more depth, allowing Sugar to scoop out all of the water and providing me with a clear indicator that she needs more water.