I believe I can provide some insight into your question. But before answering, would you please provide me some info. I would like to understand the typical training that a student goes through in your school to get to blackbelt. Let's assume an above-average student (i.e one that is enthusiastic, has good attendance and is fairly athletic.)
Average number of years before promotion:
Average hours per week of training in the school:
Average percent of time in the school practicing kata:
Number of empty hand kata learned:
Number of weapons kata learned:
Please answer these (estimates are great) and I can give my perspective on this problem.