Because people will pay to watch athletes, but won't pay to watch battles.. Besides, most soldiers spend a lot more time sitting around, doing drills, etc. than they do fighting. Even if you were to broadcast an army, most people would find it very boring. (But the soldiers, going into battle, would not be bored.)
Professional sports is big business. There are huge profits involved, the only profit in military are the selling of armaments (bombs, jets, guns/bullets); the military man does not share in that. The top brass might when they retire and start to work as advocates for those companies.