The bench press is often neglected in main site programming for CrossFit due to equipment limitation. However, using the bench to strengthen the shoulder girdle is advantageous when an athlete performs a shoulder intensive workout with pullups, dips, muscle ups, and pushups. By increasing bench press numbers, an athlete will see gains in other movements as well.
Rippetoe’s explanations seem to be the best for this.
Remember, always use a spotter when lifting heavy. Always warm up your rotator cuff using these warmups so as not to damage the shoulder. Pairing bench press with a pulling motion (such as a pull-up) is preferable.