There was one time when they were explicitly allowed to be used as paddles during the Cardboard Boat Race (otherwise the boat, including its means of propulsion, had to be made entirely from cardboard, PVA glue and duct tape).
Then they changed the rules to allow any safe means of propulsion ("safe" essentially meaning "not an outboard motor, you idiots, there will be people in the water"). Canoe paddles were the most common, but I also saw pedal power, paddle wheels powered by electric drills geared down through a bicycle transmission, and one boat towed by a scuba diver at the bottom of the river...