It would cost a shitload. Morgan City would have to be build up tremendously, since that is likely where the bulk of the flow would end up, through the Atchafa

It would cost a shitload. Morgan City would have to be build up tremendously, since that is likely where the bulk of the flow would end up, through the Atchafalaya river, basin, and delta. New Orleans and Baton Rouge would see one of the most dramatic economic implosions seen in the modern world. Akin to, and possibly worse, than the hollowing out of many formerly prosperous rust belt cities. There would also most likely be a lot of people displaced by allowing the Mississippi/Atchafalaya to meander at will, since the channels to handle that amount of water if left to its own devices are simply not there. You'd end up with an absolutely enormous floodplain between the current paths of those two rivers. My family is from the bayous between that area. The highest place in town was an artificial hill in a park 20-30 feet high. All in all, it's probably better ecologically to simply let the rivers meander as they will, but economically it is in the city, state, and region's best interests to maintain the status quo.