If there is a public trial, it makes a big difference. If a drone saps Khameed Al Unpronounceablename in the mountains of Yemen, it is in the press for maybe one day. If a live prisoner is tried in a court it is in the media for weeks, with all sorts of prpopaganda on both sides. If the US makes a presumption of following its own laws, then it is important to do so.
This is just as much a propaganda war as it is a fighting war.