A centralized organizational structure is only efficient if the folks making the ultimate decisions can handle that duty. Look at World War II as an example. American field commanders had more authority to make snap decisions than did their German counterparts leading to a situation where the German army was not as responsive as it could have been.
The Normandy Invasion is a good example of how that worked. When reinforcements were needed to fight the Allied troops as they stormed the beaches, the authority needed to move those reinforcements rested with Hitler. As he was sleeping at the time and left orders not to be disturbed, German units that could have been instrumental in turning back the invasion remained stationary and effectively worthless in early stages of the campaign.