Similar to a college degree, any style of martial arts can takes years to fully grasp and master. The black belt, or any other similar ranking, is not something which is obtained overnight. Often it can take years of frustration, tedious work, and practice until one achieves a skill level on par with the standard a black belt has. Give someone 2 months and they can probably remember the forms or kata, but it can often take years before they can either practically or demonstrably apply their techniques. Often times a good measure of how well an individual knows or can apply the techniques is through competition; going to one every few years to see if they still match up to the standard, which again, is universal for all styles of martial arts.
Often times, most especially for children, tournaments are unattainable. Either they cannot pay for the registration fee, or the travel alone is too expensive. Furthermore, there is a vast amount of extraordinary fighters or performers who are unable to attend tournaments in the United States due to struggles with visa applications. Essentially, potentially the greatest martial artists have no ability to prove or demonstrate their skill, hampering their own progression as well as the progression of the martial arts world.
Part of what schools, public, or private, strive to do, is develop character amongst their student populations. Exams and essays can only do so much, however. And often the most memorable moments any child can have are ones which do not pertain to such. If a child is to know how to struggle, how to strive, and how to succeed, competitive sport is required. And martial arts can be an exceptional outlet for any such goings.
Every child has in them a lion, that wants to burst out and demonstrate to the world its prowess. If society is to continue to improve, then their spirit should not be quelled, but encouraged, and refined. As parents, it is our job to ensure they can.