I suggest for that you review your PPS-I manual and look at the different ways indicated for breathing in it. We do not say that one must breathe in through the nose and out through the nose at all times. There are so many ways to effectively use the respiratory system and strengthen in. But to answer your question, one value of breathing in through the nose and out through the nose is that it is more difficult to breathe shallow. 

It also keeps the breath more focused in the body and it requires control and awareness to keep the breath in and out. Also, when we breathe in through the nose and out through the mouth, one can keep the breath in the upper lobes and may breath shallowly. However, if taught correctly a deep exhalation, especially on strenuous exercises, though the mouth can facilitate deep abdominal contractions and a good forced exhalation.  This facilitates exercise execution many times. Specifically, we say to breath naturally (in and out through the nose), percussively ( in through the nose and out through the mouth but it can be out through the nose too) and silently (pausing with the breath or holding it).

Play with these different breathing concepts and see how they affect the exercises for you. For example, exhale deeply through the mouth on the return in the Stomach Massage Series and the Knee Stretch Series. It really helps! One thing though, when exhaling through the mouth don’t over emphasize a mouth position or alter the face, just exhale through the mouth simply. 

Good luck with your inquiry in "breathing," but remember; don’t get too caught up in it. The different elders will tell you that Joseph Pilates did not overly focus on it but let it unfold through the exercises with full inhalations and exhalations. Breathe well.