The evolution of military education is rather fascinating when you really dive into it. Your points on the comparison between ancient military education and today is very accurate. As you put it, this seems to be a transition between the physical and the intellectual although anyone serving in today's military will argue it is still about the physical conditioning to fight.
Helmuth von Moltke (the Elder) began to change how the Prussian (and German) military approached education with the study of the military plans of potential enemy's such as France. By the American Civil War, our military education at West Point seemed to focus a substantial amount of time on the science of war; artillery, topography, mathematics, ect., (Freeman, n.d.). Two areas that seem to be lacking are leadership and critical thinking development, or at least an overt effort to develop these skills as we see in today's military education.
How do you think the lack of focus by our military academies on these to areas in particular impacted, say Civil War commanders, ability to lead in combat with the onset of war. After all, many of the significant military commanders in the Civil War experienced combat in the Mexican-American War.