We gotta do this clause by clause:

• "its people have shared a history of common struggle and achievement" - no. Aside from the long history of dispute about who born in the United States really "counts" as an "American", there has never been a common struggle.
• "carving communities out of a vast, untamed wilderness" - no. As of this writing I have finished reading the first half of the document and there has, as yet, been no mention of Indigenous peoples. (Also, see the vast literature on the relationship between expansionism, the "frontier", and American exceptionalism.)
• "winning independence and forming a new government" - dramatic oversimplification. Interesting fact about this document: in contains almost no references to state government.
• "wars, industrialization, waves of immigration, technological progress, and political change" - not highlighting this because it's wrong, but because it implies a strictly linear progress of history that is typical of American exceptionalism and intellectual arguments for racism, colonialism, etc.

All in all, what Luke said.