M609 - I think what you describe by e,g,
and even on straight sections of stars some customers often wandered off centerline 2-3nm,
is something pretty weird going on, and it either creates big questions about how crappy nav gear they have in [some] airliners, or the pilots weren't using it.
I know that INS (without GPS corrections) can easily be a few nm off track on oceanic routes but this should never happen over mainland Europe.
Basically, when the procedure track is loaded (either from the database or by manually loading the waypoints) the aircraft should be within about 1/4 mile on all sections where major turns are not taking place. That is where I would be, with a crappy mid-1990s GPS and a late-1990s autopilot.
And I have no GPSS / roll steering. All modern jets (those that can fly holds on autopilot for example) ought to have computed turns.
Something very weird is going on...
What seems to have happened for you with PRNAV introduction is not really PRNAV introduction but a change of cockpit procedures to actually use the stuff they have had for many years. Even with VOR tracking one should not be 2nm off track (at say < 30D) unless somebody is not paying attention, or they are using a dodgy avionics shop
PRNAV is a boat which left the harbour about 15 years ago. The fact that GPS/RNAV approaches are equivalent to RNP0.3 makes PRNAV, with its massive costs, a pointless exercise. Even at GA level, PRNAV cannot be done for less than 5 digits and for most IFR aircraft it will mean a huge retrofit - for no extra functionality but just to get the "boxes" for which the manufacturer has produced the PRNAV LoA (etc). But in this business there are always people who are looking for work and PRNAV is a good gravy train to jump on. Almost as good as AIDS research...