Whale upper jaw and baleen plates
Whales and Whaling pictures

Long Island shore flensing a whale. Here the head of a large Right or Bowhead whale has been removed from the body. The baleen plates can be see sticking upwards (the head is upside down here), baleen was a very valuable and worthwhile part of the whale in the early days of whaling, but as time went on and substitutes appeared, it became less important eventually being discarded as not worthy of the time spent in recovering and cleaning it. 

Shore based whaling was always more small scale usually carried out by subsistence level fishing communities and so in these circumstances, it has more likely that as much of the whale will be used as is possible. Flensing in the shallows allows the huge weight of the whale to be manipulated more easily by ropes attached taking advantage of the buoyancy in the sea.