There is value in both quality and quantity. Quality is what we want to do when we want to grow. Quantity is what we do in order to engrain the information to our bodies. It's important to have both, and not just one or the other. Should we have a lot of one and not of the other, we cheat ourselves out of growth. The importance of the two together is that they encourage the individual to grow.
The thing is, we sometimes forget that and we choose one over the other. When that happens, we lose the potential, what you could have done to improve yourself. You see, running every other day does a lot for the individual in getting them back into shape, but running 5-6 days a week does quite a bit more. It allows the individual to train for longer distances. Our bodies adapt at an amazing level, and the adaption only occurs through the quantity of what we do to it. In adding the quantity and quality to the workouts, people grow and become athletes.
Dedication to both quality and quantity is also important because should you miss even one day, it changes the direction of the workout and what you want to become (the same goes for anyone that has any sort of dream towards some goal). Anything and everything you do changes the direction of where you're going. Of course, both quantity and quality effects each other, as well as the overall goal. Yesterday, I ran 7.85 miles in 58:46, an average of 7:29 min/mile. It was a really fast pace where I put a decent amount of effort in. After such a workout, there ought to be some sort of rest. However, today, I chose to go out and run 3.86 miles in 29:47, an average of 7:42 min/mile. Not too fast... but not too slow either. The important thing wasn't just the quality of my run in this case, but the quantity. I did that run today because my overall goal was to get to a point where I can run that 100 mile race. A person does not just up and run such a race without a good amount of mileage in ones legs. With that kind of goal, it's no wonder people do back to back runs. There is value in both quantity and quality.