I must say I think dredging really can be part of the solution. Much as people mention bottle necks, if these are reviewed as a riverwide scheme benefits can be obtained. It's illustrative to examine the case of the River Serven, not that many years ago flooding in Bewdley, Worcester, Upton etc was relatively frequent. The effect of the works undertaken (principally, although not entirely, construction of higher permanent and temporary defences) is to increase the speed the river flows at, therefore clearing flood water faster. (I would not disagree that measures to keep the water higher in the river basin will not also help).
Switch to the River Humber, and its appreciable quite how slowly it does flow. Now examine the flood risk eminating from its tributaries, for instance the Ouse as it passes through York. I was surprised to discover that 40 years ago 13 large dredgers were used to dredge the Humber, which clearly is not going to remove mere centimetres. I had a lengthy conversation with an engineer who worked on the Humber estuary hydrodynamic model when the bridge was being constructed, and at that time the river did indeed flow appreciably faster, and the modelling showed this to be an outcome of dredging...