alt Hacker News"it needs to maintain an actual population there and provide basic services to it. It's a fairly well established geopolitical principle."
I don't think that's true.
See the middle paragraph of page 46 here: https://icj-cij.org/sites/default/files/permanent-court-of-i...
The ICJ said that sovereignty over "thinly populated or unsettled countries" can be sustained with very little actual exercise of sovereign authority. It upheld sovereignty over unsettled portions of Greenland. They later used the same principle talking about islands that were "uninhabited or not permanently inhabited".
You seem to be saying there's a general requirement that every part of sovereign territory must maintain a resident population AND that the government must provide certain 'basic services' there. But that doesn't seem to be true, at least according to the ICJ.
If what you said were true, then no state could claim sovereignty over an unhabited place. But that's not true. The ICJ ruled that Malaysia had sovereignty over Ligitan, even though the island has a population of zero. https://www.icj-cij.org/node/103163
I somehow doubt that the major world powers that might have the capability or inclination to occupy a depopulated Alaska or Nunavut would put much credence in or be scared by a strongly worded opinion issued by the ICJ. One of them is busy trying to invade their European neighbor right now with bloody results. The other one is on a major island building project in the South China Sea turning sandbars and coral reefs into air bases to claim the oceanic territory.