NavList:

Point taken, with caveats:

1.  Its unrealistic to expect too much accuracy, especially when it comes to hand-held compass bearings converted to true (from a small-craft sailor's perspective from a pitching deck, without gyros). 

2.  By the time you have worked out where you were you're not there any longer, usually.  If you want to know where you currently might be then you need to run that position forward along the craft's assumed (again, excluding electronic assistance, most likely a compass bearing converted to true) track according to estimated average speed over the period.  So even if your last fix was quite accurate that benefit has been lost during the necessary approximations made to derive current position.

3.  Why do you want to know where you are?  It might be to avoid some proximate danger in which case, apart from anything else (and again from a short-handed small-craft perspective) you could be better off getting your nose out of the chart table and on-deck keeping a keen eye out.  For example.  Mostly, however, the reason for wanting to know current position is in order to know how best to get to where you want to go.  In order to calculate the future bearing to follow, in other words.  In that case, whether a fix made along the way based on shore NAVAIDS is particularly accurate or not makes little difference to the track to be followed, or the calculated time to get there.

Is the assumption here that a systemic error needs correction?  If that is the case, then correcting for systemic error leads to a fix in the centre of the triangle, and is the classic solution.  But perhaps I've not understood this...