Greenland is very strategic territory and becoming more strategic by the day (due to global warming). It is one of most important locations for a military presence. And it would be extremely undesirable (to the U.S.) if a rival country had a significant military presence on Greenland.
But Greenland needs a lot of development. Its 56,000 inhabitants need better resources. While the average Greenlander has an income of $35,000 (more than half of what an average American makes), it takes a lot of resources to live in a place that has such extreme weather.
So here is a modest proposal: Greenland sells itself to the United States.
Yes, the first reaction might be that I’m a jingoistic crazy. But this could be good for every Greenlander.
Imagine selling Greenland to the U.S. for $120 billion (assuming the Danish allow the Greenlanders to make that self-determination). That means that each Greenlander will be worth $2 million — including every adult and child. They could even set up a trust for kids (so the kids, not their parents, have access to the money.

Greenlanders are a proud people should not crassly just auction off their sovereignty. But Greenland is not sovereign today (their are “owned” by Denmark). They rely on Denmark for significant funds and must constantly please and lobby the Danish parliament. With a net-worth of $2 million, Greenlanders would have full self-control on how they want to run their society.
Greenland would be, by far, the richest place in the world. $2 million net-worth per person far exceeds even the wealthiest enclaves. Imagine what Greenlanders could do.
In addition to the money, all Greenlanders would be full U.S. citizens. So, if they wanted, they could move to Florida (with their $2 million each) the next day. Regardless, they could rely on the safety and protection of U.S. citizenship forever.

Your thesis first off tends to discard the fact that Greenland is a self governed part of Denmark, which does have its own governing body and self determination. It is therefore not to Denmark to sell it at all, and the population would clearly loose out on it too ( which is their local feeling)
Maybe this colonial idea makes strategic resource sense for a colonial power, but one would have thought those days to be over. Executing on it, would see America opposed by every other nation in the world, and likely herald its demise altogether. That is what colonialism did to the powers of the nineteenth century.