Everything in Alaska is expensive. It all comes from far away into a very spread out area with difficult terrain and weather conditions. Many places can be reached only by air (quick but expensive) or, in some reasons, barge or ice bridge. In the bigger cities (Anchorage, Fairbanks), things are pricey, but the smaller villages are eye-wateringly expensive. My brother and I paid $4.50 for a single warm can of Shasta Root Beer in a small village in Southwest Alaska. We saw a bag of Toastitos going for ~$15.
At these prices, even the boxes and packing tape are going to hurt a bit.
[0]: https://ballotpedia.org/Alaska_state_budget_and_finances [1]: https://www.google.com/?q=alaska%20population
It gets expensive really quickly.
There are no hardware stores with building materials already there, and no trees to make a cabin with. A locally sourced house would probably be a permafrost dirt hut, which would melt as global warming continues or maybe a discarded shipping container. They must bring in prefabs, just full stop.
Look at the pictures, they aren't living high on the hog, but I guarantee the buildings you see in the picture are comparable in price to the 300k/person.
Could also be that existing housing is too fragile to move, conditions are mighty rough out west.
But, it could also be a tiny bit of pork helping out some disadvantaged people in the boonies. Maybe a combination of all of them
I guess my main point is that things are surprisingly tricky in the arctic, far away from developed places