Another good point, the same sediment that raises the riverbed is essential to maintain the protective wetlands of the delta (which has been shrinking for many years).
So it is really like building on a barrier island or a sand dune, just a (probably) longer time scale before things go FUBAR.
I suppose the whole lot could be rebuilt upstream and inland, don't know if the Mississippi has worse dredging issues, etc.
But I'm sure it won't be. The cost of extending pipelines from offshore, rebuilding infrastructure, etc. (heck, the actual port structures are ABOVE the rest of the city--at sea level!--and are probably the least damaged), would be decried as prohibitive, "especially in light of the cost of the exsisting damage." It won't matter whether that argument truely makes any sense.