Name one power that the constitution denies to states, and explain how the nation benefits from that restriction.
One power that the Constitution gives to the Congress and not the states is the power to declare war. That means that the states can not declare war on foreign countries. The nation clearly benefits from this restriction on state power, as one rogue state could decide to declare war on a foreign power, dragging other states or the country into the fight. The United States has formally declared war five times in its history (during the War of 1812, the Mexican-American War, the Spanish-American War, World War I, and World War II). Generally, the Congress's declaration of war comes after the President has made a request of Congress to do so and there has already been an outbreak of hostilities. In other instances, such as Vietnam, the Congress has authorized military combat but not war. While going to war is always a fraught decision, it is more likely to be expression of the will of a greater number of people if the decision comes from the Congress than if the decision to declare war came from one or several states.
The first one that comes to mind for me is the power to regulate commerce between the states. States cannot do anything to regulate commerce between them, except if the national government allows them to do so.
The benefit to this is that it gives us one big common market made up of the whole country. A company in Washington can sell things in Idaho or even all the way in Florida. Before the Constitution was written, states put up barriers against trade with one another. This made the states into little countries, almost, each with their own economy. That retarded the growth of the US economy as a whole.
The Constitution only allows the federal government to coin money. This is quite wise for the United States, and for that matter, any nation where their economy is concerned. What if we had 50 states with 50 different currencies? We would have to exchange our money at every state border, and the states would need their own gold reserves and each currency would be worth different amounts. If another country wanted to trade with us, they would have to trade in the currency for the state they were trading with. This was a wise, wise move on the part of the Founders.