I can't believe the amount of nonsense in some of the follow-up posts.
What this link above says about blanketing, etc, is potentially correct in the context of some industrial heat exchangers.
But the reason a pressure cooker cooks quickly is because of the elevated temperature. The principle reason for removing the air quickly is that once this is done and the valve is floating on steam only, the water has reached the maximum safe temperature of the pressure vessel.
Getting rid of the air also reduces the oxidation of some of the organic matter in food.