The statement that best analyzes the political role of the U.S. in World War I is:
President Wilson was so persuasive that the Treaty of Versailles essentially restructured Europe according to American political ideals.
This reflects the significant influence of President Woodrow Wilson's vision for peace, including the establishment of the League of Nations and the promotion of self-determination and democratic governance, as articulated in his Fourteen Points. Wilson's ideals had a profound impact on the post-war peace negotiations, although the eventual implementation and acceptance of these ideas were complex and varied among the European nations.