Yes, I think training is the #1 problem. But the powers to be, as well as much of the old crowd, have dug themselves so deep that bringing it in formally is just about impossible.
It's true that there's not really an obvious place for GPS training in the PPL - it has enough content already, and personally I believe the VFR Nav must be learned, if just in preparation for the day you find yourself with no power in the aeroplane.
I guess you could add some GPS theory to the PPL Aircraft Technical exam, but why not have some kind of basic post-PPL "differences training" (coupled with an associated avionics-quality requirement) that allows you to use GPS as a primary navigation aid? That way there is a basic check that the user understands the kit well enough to avoid the most simple mistakes - and that IMHO is the real problem with GPS. As the price of a receiver drops below the price of an hour in the air I can't believe it will be ignored forever.
We cannot fly IMC or tailwheel without demonstrating competence. Why not the same thing for GPS as a primary navaid? Those with decent kit and a sign-off can join the 21st Century, the rest of us can carry on with a Pilot III as backup.