US Banks will never be bankrupt. They only need to issue more notes with their printing machines. The petro dollar is the international currency for reserve. A few billion notes won't harm the 80% of world trade.
But if Saudi Arabia, Turkey, Egypt, UAE, Qatar decide they will dump the dollar for maybe ether, then america's economy will be in deep turmoil. America's primary export item is paper notes called USD.
They don't really have much value (how much does paper cost?) but since everyone uses it, (or is forced to use it), it has a good demands.
You bet but tell that to Lehman Brothers or Bear Stearn.