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 effectively highlights the significant contributions of the U.S. in terms of resources and military support, which were crucial to the Allied victory. It also notes the importance of American ideas in the post-war peace discussions, reflecting the emerging influence of the U.S. on the global stage.