Why not just buy it?

53% of the land area in the USA was purchased. I have read other numbers, but 53 seems about right.
I think it would be up to the people of GL. Have a binding referendum. The US would give each voting-age citizen $50,000 the day GL becomes an American state. That is about 25,000 people to receive $50K = only $1.25 billion. Since the Ukraine war began, the US has given Ukraine
$175 billion. That is 140 times the cost of buying GL. We give a half dozen countries more foreign aid than $1.5 billion
every year.
Why not make the offer? Offer Denmark a couple of billion to give it up. I am willing to bet the Greenlanders would jump at the offer to not only get a cool 50K but to become American citizens with all the benefits and military protection.
In the future... just make the same deal with other Island nations. It seems we have plenty of money to give away in foreign aid... why not get something back for it?