First the bottom of the Mississippi river below Memphis is below sea level. Dedging only lowers the bottom which is somewhat backfilled from the gulf--this is already being demonstrated as increased salinity in municipality potable water suppies is being encountered along the lower Mississippi.
Second--Eads Wiers (those dikes built perpendicular to the river banks) work by increasing channel flow to scour the channel bottom. If the river surface flow isn't there because of lower river surface elevation, channel scouring won't happen. IOW the mechanical scouring of the channel is necessary because the engineered scouring isn't happening.
Additional--keeping the Mississippi open is transportation mission critical. One barge is equivalent to 100 semi truckloads or 40 train carloads. Along the Ohio, Misissippi, Missouri, Tennessee an Kentucky Rivers barges is the cheapest method of bulk freight--bar none. Losing this transportation venue, even temporarily, can be economically significant.