That is only partially correct. First, in many case, beyond just math, academic instruction does not directly apply to practical application. But, the reverse

That is only partially correct. First, in many case, beyond just math, academic instruction does not directly apply to practical application. But, the reverse is absolutely true. Experience with practical application very closely correlates to better academic performance. The key that you missed is practice. Instruction is helpful, but it isn't practice. Practice is also the key difference between graduate education and high school or undergraduate education. Yes, in graduate school there is still instruction but you are expected to use that instruction in more abstract ways to achieve some condition. Secondly, higher education is mostly about signaling. It is about other things too, but signaling is first. Examples include the social consequences of where you go to school, the major you choose, grade point average, who you meet, and so on. Compare those factors against professional education, like continuing education credits for law or medical licensing. Nobody cares about the signaling around that professional continuing education, because you are already employed and the goals of that signaling are already achieved.