I started my ten year piloting career at Potter bridge at Whitsun, 1988. Each season, Easter to November, we piloted anywhere between 10,000 and 15,000 boat passages between us. Prior to that year, Hoseasons employed two pilots and Blakes two also. In 1988 the pilot service was combined - joint Blakes/Hoseasons.
I suspect the pilotage figure is nearer 1000 a year now. Yes, the boats are bigger, yes they are wider at their tallest point, but, more importantly, in the thirty odd years I have occupied a riverside bungalow above the bridge at Potter, water levels have most certainly risen by at least an average of four inches. Back in the day, Bounty/Solar 37s, Hampton Safaris, Connoisseurs, Broom Skippers, Bounty 27s, Seamaster 27s and Elysian 27s were almost certain to get through the bridge - often even on high tide. Occasionally we even put through boats needing all of 7' 3" air draft.
Water levels have risen to such an extent that I have lifted thirty-two Thurne bungalows, at the last count, to clear them of the high Winter tide levels.
Dredging? I don't know if it would help.