Baton Rouge, too.
The Corps nearly lost the Old River Control Structure in the 1973 flood.
It wouldn't neccesarily be a dead city, or even suffer from the loss. With a pair of lochs, the old riverbed could easily be converted into a shipping canal. As I recall, the Miss is fairly flat south of Baton Rouge, so it should require minimal dredging at the upper end of the channel to keep the whole thing filled with water. One loch at sealevel, and a second where the new shipping channel meets the river, are all that would be required.
The Mississippi changes course all the time. Look upstream at the present day boundary between Mississippi and Louisiana. You will notice quite a bit of Louisiana on the eastern side of the river and Mississippi territory on the other side due to the river having changed courses so many times since the river was designated as the border. Just about every time there is a major flood upstream the river ends up cutting off loops.