Probably the formula is the way it is for historical reasons. Generally speaking, our intuition of "steepness" matches the definition of slope: the steeper a line is, the higher is its slope in absolute value. This works with slope equal to $\text{rise} / \text{run}$, but would not work if the slope were equal to $\text{run} / \text{rise}$ as you suggest. For a modern example, when you drive down a steep mountain highway, you will notice signs saying something like "Danger: 5% grade ahead.
