The are a lot of things that people eat whole, such as sardines, anchovies, and other small fish. Some cultures even use bile as a flavoring (see Papaitan from the Philippines), and others eat bugs (crickets and grasshoppers are very popular).
Our sardines and anchovies have the head and guts removed, and probably the tail. We do sometimes eat skin and bones. The same goes for canned salmon and herring.
We also peel, decapitate, and gut our shrimp. This is probably a better comparison because the exoskeleton is similar.