Those mechanisms of the market might do well in supplying soldiers to meet a demand for defense, but I'm skeptical of the ability of the blind market to plan a grand strategy or defeat the enemy in battle.

Plenty of private corporations seem to do quite well at grand strategy and defeating enemies in market competition. It doesn't seem a huge stretch to imagine them achieving similar success in battle. Much of military success comes down to logistics and I think a reasonable case can be made that private corporations already demonstrate greater competence in that area than most government enterprises.