Another reason for opening our hips all the way is so we can create an elliptical motion with our swing. When our hips are rotated a full 90 degrees, the top hand is able to reach out farther towards the pitcher, as shown below in Figure 1. This reach is called "extension through the hitting zone," the more extension, the better chance of hitting the ball.
a)
b)
Figure 1: Overhead view of extension. Without opening hips a), and with opening hips b). Click to enlarge images.
First, let's examine what happens when you don't rotate your hips, and why it's harder to hit this way. For argument's sake, let's assume that a batter has no hip movement at all, and uses just her arms. It would look something like this <here>
Note: This swing does not generally provide much power since the hips are not utilized, unless the hitter has a very strong upper body
Figure 2: Schematic of overhead view of circular swing. The sweet spot denoted by the green section on the bat traces the circle around the hitter. Notice the ball which travels in a straight line only hits the sweet spot twice on the circle. Click to enlarge image
Figure 3: Schematic of overhead view of elliptical swing. Compared to the circular swing, the sweet spot is more in line to the path of the ball. Click to enlarge image
In summary, our goals as hitters are to first create separation between the upper and lower body for the X Factor Stretch resulting in power, and second to have the most extension through the contact zone as possible, resulting in more consistency.