Why Do Accessory Work?
Weightlifting requires a lifter to be strong, fast and coordinated. Mentioned in the S.A.I.D Principle, the body adapts to the stressors applied to the body. Why not just train The Snatch and The Clean + Jerk since they are the most specific?
Fatigue plays a large role in training and the ability of an athlete to maintain intensity. What pace could you run 50m? Compare that to the pace you could run a mile. For the mile, you would have to run at a slower pace than 50m since that speed/intensity could not be maintained for that distance. Same is true with barbell movements. When more reps are performed, something will have to give; load used, the speed of movement, and/or the coordination of the movement. The Prilepin Chart is a good reference for the optimal reps completed for a given load.
Then how do you continue to add volume and progress the lifts? You add accessory work to address the weakness of the lifter. Accessory work that is the most similar to the lifts will likely have the greatest transfer to the lift (Squats, Snatch/Clean Pulls, etc.), but should not be limited to these lifts alone once the lifter understands how to properly perform the lifts. Have you ever watched an athlete who lifts well up to 90% and then mechanics breaks down? Sometimes the lifter may just need a cue as a reminder, but more often than not, there is a weak link in the chain and addressing the weakness will have a greater effect than cueing the athlete. With a strong understanding of the mechanics of these movements, a coach should be able to identify the weak link and apply a "special" exercise to bring up the weakness. If done well, this will improve the lifters form in the lift better than a cue.
Another important reason to use accessory work is to maintain the health of the lifter. Weightlifting is repetitive and can beat up the body. We feel that some time should be spent on exercises that maintain balance and prevent injuries. Giving up a little time will be less than the time given up if the athlete is unable to train.