In order to shoot fast, you have to see fast, and in order to see fast, you have to shoot fast. Airsoft is an excellent resource to develop your ability to see fast.I remember reading about a professional shooter, maybe steel challenge, who did most of his practice with airsoft because he lived in Japan or something.
Think about what happens to your visual perception after a long bout of highway driving. Initially, the 70 MPH you are doing looks and seems "fast", however, over time, you adjust visually, and that speed no longer seems "fast", and given enough time, it can actually seem slow. Airsoft is an excellent tool that can be used to achieve this effect, as they can be used cheaper, more frequently, and in more places than live rounds.
Airsoft is an excellent way to develop your ability to see faster, and when you can see faster, it makes it much easier to shoot faster.