If "our major concern" in this matter should be the U.S. Constitution, please show me an article and section, or amendment that permits the government's indefinite detention of a person without indictment or formal charges, without a right to counsel, without a trial, and without due process.

And there are obvious reasons why we can not disregard the Geneva Convention or international treaties and law. As we have been the most militaristically engaged nation in the world since the 20th century, we have had, have and likely will have the largest number of armed personnel across the globe. Failure to abide by the convention or international law is an invitation for nations around the world to do the same.