The reasons are clearly stated. Mental clarity is not one of them. Not even as a by-product.
Athenian: "Physical training was seen as necessary for improving one’s appearance, preparation for war, and good health at an old age."
Spartan: "The pursuit of intellectual knowledge was seen as trivial, and thus academic learning, such as reading and writing, was kept to a minimum. A Spartan boy’s life was devoted almost entirely to his school, and that school had but one purpose: to produce an almost indestructible Spartan phalanx."
"men sana in corpore sano", my dad used to say :)
[1] http://en.wikipedia.org/wiki/Education_in_ancient_Greece