But the goal isn't to catch up on knowledge that the student should've learned last year. That should've already been addressed through holding the student back

But the goal isn't to catch up on knowledge that the student should've learned last year. That should've already been addressed through holding the student back, summer school, tutoring, etc. If the teacher has to not only teach this year's material but also reteach last year's, that's not fair the students who need to learn this year's material. Grading isn't just a feedback mechanism. It also is an incentive. When you say "only the final test matters", then young students (who probably haven't totally grasped long-term planning yet) have not as much reason to care about learning the early material until it's too late.