I'm not certain, but believe that there are various spillway outlets along the river to address some of that kind of flooding (or at least the downstream flow of floodwaters.) North of Baton Rouge they Army Corp of Engineers has had diversions facilities for years to channel excess into the Atchafalaya River (roughly a 20 mile wide swamp that would now probably be the Mississippi River if not for intervention.) IIRC there is similar between Baton Rouge and NO, but could be wrong about that.
There is this critical breakwater dam on the Mississippi (maybe 150 miles up or so, I am not sure), thwarting nature because the natural slow of the Mississippi due to silting is now due south from that dam. Thus that dam is under tremendous pressure, which if it fails will cause the Mississippi to flow down the Atchafalaya River whipping out everything in its path, including I think Morgan City. Louisiana is a state insurance companies should avoid.