When you said "It's a fairly well established geopolitical principle." I assumed you were talking about the legal aspect. That's why I responded the way I did.
Now I understand you're talking about not about the legality, but the practicality. That's even easier to refute I think: if a world power wanted to annex that part of Alaska, the ~4000 current residents of Nome wouldn't be much of a deterrent, even with their hunting rifles.
No, they certainly wouldn't, but in the realpolitik of war, they would provide the justification for the USA to engage in an armed response to retain the territory. Basically think of the two scenarios of what would happen in the Falklands in 1982 if either:
a) the islands were claimed by the UK but also completely unpopulated and were occupied by Argentina
or
b) what actually happened, the islands were occupied by almost entirely UK-descent, English speaking subjects of the Crown, resulting in subsequent military action that had broad and overwhelming public support in the UK.