Mike
The way is open for instructors and schools to run post-PPL navigation courses, including the use of GPS. I don't see them advertised, which is a pity as there seem to be many who would benefit.
IMV, the reason these things never take off (and I have been to Irv's courses a few years back) is that the pilot doesn't get any privileges as a result. So why should he bother? I once went on a 1-day GPS course, run by Honeywell, and nobody else turned up. Etc.
Compare this with gliding. I don't glide (well I hope I never have to

) but I gather they run a system comprising of a string of grades, so there is a continual incentive for people to keep improving.
There are just two reasonably accessible post-PPL "grades": the night and the IMC rating. The first is crippled by most airports closing early, and the 2nd is crippled (mainly, IMV) by non-availability of half-decent planes for rental.
WR
For IFR flight, by definition you're head inside the cockpit
Do you have a reference for that?

Actually, the great majority of IFR flight is in VMC. That is the #1 planning objective; the alternatives involve potential continued flight in icing, etc. And anytime you are in VMC you are supposed to keep a lookout - even under IFR/airways.
I don't know why so many people think that anything to do with IFR means looking down and fiddling with knobs

One actually does very little of that. IFR nav techniques are absolutely brill for VFR flight. I stopped dead reckoning the day after my PPL skills test, have never been lost, never been uncertain of position, never infringed (as far as I know). GPS is a part of that, only a part. Even dialling in a VOR/DME makes a dramatic difference to navigation confidence.