One big reason is preparation, people start preparing for tests 2 to 3 years in advance. And the method of testing influences exams used in grades before as well.

So assume 4 years of high school and someone that just came in. They are still preparing for SAT like tests in their first year of high school. Someone in final year of high school is well trained in it. So even though the benefits do not carry, enough portion of incoming students are still reaping benefits of standardized tests. The decay only shows later when batches without any benefits of standardized tests are coming through.