The bible totally ignores the new world because the new world was a non-player(insignificant) in the days prior to 1000AD. In the new testament and in Revelations, it is still ignored, because in the end days, the new world will AGAIN be a non-player. The USA will not exist as a world power in the final battle and will not participate.
I wondered about that part too, and thought of: 1) America is neutralized by a massive nuclear strike; or: 2) Yellowstone blows apart, covering a large portion of the Lower 48 with volcanic ash.
I agree that nations will not be important after such a conflict and Isaih says they beat their swords into plowshears and spears into pruning spears. Society will be focused on quality of life technology instead of military.
On your second point, I disagree. We not only will be involved, we already are. Revelations says the flash point of the global conflict is river Euphrates that sits right smack in the middle of Iran and Iraq. There are four angels unbound which are keeping things from going hot before their scheduled time. America will be in Iraq for a long time and we are already at de facto war with Iran.