semantics
what I mean is that a skater that goes into an international/continental championships where skaters from all countries go to have a different sense of pride.
For instance, I am sure the 4 Russian ladies were proud to be at GPF but their agenda was to place for themselves, get prize money and ranking points... but at Olympics or worlds and even at Euros they represent also Russia...
The GPF is not open.. it's an invitational event based on GP results. No American ladies were there this year. No Russian ladies were there some years... so it's not so much an event where National pride and representation is a factor.
That's what I mean with skating for their countries. Sure you can argue that they always do... but it's not really the same in events where over 20, 30 or even 40 countries are represented than it is in an event where 3 4 -5 or 6 countries at best are represented.
I hope I clarified my point.
YMMV
ETA forgot to address one of your questions : the timing of nationals... of course it has an impact. For ISU championships, athletes are named by their country's federation... so there is even more of a hype about those events and the fact that they happen shortly after nationals... actually the nationals are shortly before the bigger events

so that skaters best in shape are chosen.
For GPs... it's a different system based on individual results. A skater can fell national pride while on the tour but he/she is there based on personal results, not based on national team selection.