Geologist here: while overly managing of the Mississippi does make a difference, that only controls where new sediment gets deposited. Even if new sediment was deposited in sinking urban areas, it wouldn’t ameliorate the problem of subsidence because it would be deposited on existing infrastructure, burying it.

The real reason for the subsidence is that the sediment that makes up river deltas slowly compacts under its own weight, expelling pore water and becoming more dense. This is natural and unavoidable, although it might be marginally enhanced by oil and gas extraction (it is a bigger problem with groundwater withdrawal in other areas).