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Back to the original question, of whether you should know your exact location. For the purposes of Firecontrol, Yes, its reasonable to know and IRL i beleive there was device called the " Dead reckoning tracer" that could automatically plot ownship location onto paper.
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There was a DRT in the conning tower and there still is (or was in the 1980s) in Control. The modern Geo Plot is kept on top of it at BS. In normal steaming the nav chart is laid over it and the "bug" is lit and shines through the paper.
The DRT is a waist-high cabinet full of gears and sychros. It has a plate glass top and two internal sliding bars, sort of like the guts of an Etch-A-Sketch, are driven by the clockworks in precise directions and speed. At their intersection is a small device carrying a tiny light pointed up through the glass--this is called the "bug". There are cranks on the exterior to drive the bug to any location. This is useful when a nav chart is over the glass and the bug has to be slewed to the location of a new fix.
The DRT was reset after every fix, either celestial, radar, or visual crossed bearings if near a landmark. It then took inputs from the speed log and gyro compass to dead-reckon current position. It did not account for wind, wave, or current, so it slipped over time. Every prudent navigator never fails to grab a fix in EVERY case presented. Not knowing where you are against a lee shore has been a CO nightmare for thousands of years.
As for fire-control and knowing where you are, who cares? If there's a landmass or shoals nearby mark them, but the FC solution is all relative anyway. A modern geo plot is done on blank tracing paper. You know the target is X yards away at Y bearing. Pick a blank piece of paper and mark him those coordinates away from the DRT bug. Lat and long don't enter into it. Torpedos don't speak lat and long.