The statement that best analyzes the political role of the U.S. in World War I is: "Without U.S. manpower and supplies, the Allies would not have won the war, so the Allies thought it was important to use American ideas."
This statement reflects the significant impact that U.S. involvement had on the outcome of the war. The entry of the U.S. into World War I provided critical support to the Allies through troops, resources, and supplies, which helped tip the balance in favor of the Allies. As a result, the Allies recognized the importance of incorporating American ideas into their post-war plans.