The deep ocean is actually something of a desert so far as fish are concerned. The water is too poor in nutrients to produce much phytoplankton, which is the start of the food chain. If you were to randomly lower your fishing lines or a net in the middle of the Atlantic, you would not catch much.

Almost all the world's major fisheries are coastal, or at least on the continental shelves. There are a few fishing spots in the open ocean as well, but these are special places which exist only because of localized undersea structures (basically, subsea mountains that force currents upwards along their slopes, bringing nutrients to the surface). You could certainly fish at these locations, but you have to know about them to go to them. They are tiny islands of marine life in the middle of vast deserts.

Also remember that merchant ships and passenger ships are not fishing vessels, and lacked the equipment for more specialized fishing (trawl nets, traps).