NavList:

In the middle of the ocean it doesn't matter.  Approaching the Minerva reefs, Tuamotus or Chagos Archpeligos it matters greatly.  All of these are low lying or awash so a navigator on a small vessel would want to be accurate to several miles rather than 10nm.  

Approaching the Tuamotus at night on would want to heave to an wait for daylight before approaching and entering.  The currents in this area can be very random.  You might think that stopping 20nm from the atolls would be sufficient but if you are actually 10nm or so closer, between 0000 and 0700 you could be swept 14-18nm closer whch would put you into the atolls and shallows.

There are plenty of places where you want better accuracy or at least a better idea of what the errors in your position are likely to be.

Re: Position errors for 2- and 3-body observations
From: Randall Morrow
Date: 2017 May 16, 17:46 -0700

I have to tread carefully because I am likely the weakest mathmetitcian that ever posted here. There have been several posts about errors in the "cocked hat" and like this one, all over my head. Pun intended. But to my point. I have done over 6000 sights with an artificial horizon and always used the obvious center of the hat triangle as the fix. It is always within 5 miles or so of GPS. There is uncertainty of course, but in mid ocean, does it matter? If it's within 10 miles you're OK. Right? 

Regards, Randy