Practice makes perfect, or so the saying goes. But what are you actually accomplishing from repetitive practice? Hours of drills are necessary to achieve mastery of any skill, yet the hours of practice do not necessarily lead to proficiency.
According to Malcolm Gladwell, most masters of their craft have put in roughly 10000 hours of practice prior to mastery. However, those 10000 hours can't be mindless, rote repetition. What separates the amateur from the expert is the thousands of hours of mindful training--it's 10000 hours of focused attention to perfect practice that develops highly refined skill.
Repetition provides a controlled environment for practice. With the complexity of variability removed, the practitioner can more readily train the mind's attention to notice every detail. The mental training focuses the mind to expand the practitioner's perceptive abilities. The diagnostic eye of the doctor, field vision of the quarterback, attentive ear of the musician, etc. are all perception skills honed over countless hours of practice.
For physical skills like martial arts, the mental development is also accompanied by neuromuscular adaptations. The body and mind are inherently plastic rather than rigid. The more movements are practiced, the more efficiently the neural wiring organizes for that movement pattern. This adaptation to repetition is a double edged sword: just as desired movement patterns can be trained, incorrect movement patterns can also be ingrained; the attention to correct practice is important.
Attentive practice is also necessary to ensure the development of true skill as opposed to conditioned reflex. Rote practice without attention develops a response skill which may or may not be under conscious control. Reflex can be effective, but does not lead to skill. Since it is not under conscious control, the reflexive response fires regardless of the conditions; it does not reflect any awareness or understanding from the practitioner so much as programmed reaction.
Repetition is simply a tool to training a skill. The goal is not mastery of a drill, but rather the use of a drill to groove efficient movement patterns and heighten perception. Like any other tool, repetitive drills have their place. The aren't the only path to skill, but if their use is understood, they are an effective tool for facilitating skill development.