Aristotle and physical education

Running the mile was perhaps the most dreaded part of P.E. for me when I was in middle school and high school. Students ran the mile, but as far as I remember, there really wasn't much time spent on preparaing the students or training them to run a mile. At least not that I can remember. It was a part of the quarterly (or semester) physical fitness exam. I didn't get much endurance or cardiovascular training until freshman year?

Is running a mile under a certain amount of time really indicative of general fitness? If so, then why didn't we run it more often, and do more to prepare for it? If not, then why was it part of the physical fitness exam?

Aristotle writes in the Politics (trans. Peter Simpson):

The gymnastics is to be employed, therefore, and how it is to be employed is agreed: up to puberty the young must be put to lighter gymnastic exercises and be kept away from forced diets and constrained toil, so that nothing impedes growth. That growth can be thus impeded is indicated by no small sign, for one could find but two or three who have won victories both as men and as boys in the Olympic games, because the constrained gymnastic exercises of their training in youth took away their strength. But when, for the three years after puberty, they have spent time on other subjects of learning, then the age following can fittingly be taken up with toils and constrained dieting. For one should not impose toil at the same time on both thought and body, as each naturally works the opposite effect: toil of the body impedes thought and that of thought impedes the body.

What would Aristotle make of grading or measuring the students' physical fitness, or requiring students to be able to run a mile under a certain time in order to pass? Is he justified in his opinion that males should not be undergoing extensive training until later in puberty? How would he judge contemporary American physical education? Has anyone written extensively about the gymnastic exercises of the ancient Greeks? Wiki entry on the gymnasium. Have ancient Greek theories about exercises been superceded? Are physical drills better than strength exercises?