One would think that different priorities are at work today already. Leadership positions in practical life are given more often to strangers than to one's "own" folks: business leaders virtually never emerge from the ranks of the company they are supposed to lead. That's another human "necessity" at work - bitter jealousy, and a strong faith in grass being greener on the other side (even if all other change is frightening)... Outsourcing of leadership is found to be practical and conductive of harmony and confidence in the leaders. Heck, Peru imported a president recently... And never mind the thousands of leaders who have imported themselves to the throne by force.
In "Wolf in the Fold", Argelians readily outsourced their security to Rigel and other foreign worlds, and nothing hinted at these prominent de facto planetary leaders having to assume Argelian citizenship in order to boss around the locals. It's not a case of distribution of labor within the Federation, either, as neither Argelius nor Rigel II was indicated to be a Federation world. And even if it were, we'd still have a clear example of the people of the future just not caring.
The pair of words "Federation citizen" appears often enough in modern Trek, yes. In most cases, the context is one of seeking legal protection (O'Brien in "Tribunal", Bashir in "Inquisition", John Doe in "Transfigurations"). But the context is also one of getting none, as the interstellar "partners" of the UFP demonstrate no respect for the supposed rights associated with UFP citizenship. Then there's the trope of the rebellious colony: UFP citizenship just doesn't appear to be a popular thing to hold, and rather paradoxically the keenest adherents turn out to be the Maquis, when in need...
Nog was probably a Federation citizen
Not in "Heart of Stone" yet:
Nog: "All right. Where do I sign up?"
Sisko: "It's not that simple. As a non-Federation citizen, you need a letter of reference from a command level officer before you can even take the entrance exam."
Whether you have to get the citizenship before you start serving in Starfleet, we never really learn.