As severed fins could be easily stored, it made economic sense for fishing vessels to remove the fins at sea, rather than bringing the entire animal - which would quickly fill a vessel's cold storage areas - into port.
Organizations like Sea Shepherd, Greenpeace, The International Fund for Animal Welfare, the Humane Society and -- yes -- People for the Ethical Treatment of Animals all campaign in various ways to stop the decimation of whales and other intelligent creatures of the sea.