This is reprehensible, but I can't help but wonder if the fact that we're reading about this is related to the recent rhetoric about Trump "liberating" Greenland.
If this is true it takes Greenland from someplace not worth worring about to something we should want. Though even then I think Canada is better placed to take over, and ending the Whisky war (then I double checked and turns out that ended a couple years ago...)
As a Canadian I can tell you we've done all the same things to our Inuit and First Nations generally, and probably often worse. And I imagine there's similar crap in Alaska.
FWIW my parents did a trip up to Baffin Island and then across to Greenland briefly some years ago. They said the living standards of the Inuit on the Greenland side were immediately and obviously much better. Better housing, infrastructure. They shared their photos.
That's not to say the Danish are saints. They are implicated in the same kind of colonial shenanigans as Canadian settlers.
In any case the US has no business there.
There does need to be stronger trade links between Canada (and the US probably) and Greenland. Canada only just now opened a consulate there for the first time in history. Same with cultural and linguistic links, I would expect as well.
I was watching an interview with a Greenlandic politician and he was pointing out how right now all trade between Canada and Greenland goes through Denmark first and then to Greenland. Which is preposterous considering proximity. Canada has a free trade agreement with the EU, and therefore Denmark and therefore Greenland, but the physical trade infrastructure is inadequate.