USA, since wwII have had permission to put whatever bases and installations into Greenland. The most important ones being the Thule airbase and the QEW radar installations. BTW, there were Thermonuclear bombs at Thule air base.
Denmark is fine with that, as a good ally. And I am sure the Greenlanders are happy also, because it provides employment for them.
That is why USA do not gain any security advantage from taking Greenland. So why piss off one or more of the loyal, actually servile, NATO partners. Denmark is vital to NATO because it monitors the entrance to the Baltic Sea, and operate listening posts in the Baltic. Maybe with all the satellites that has become less important.
While the Danes are not gaining any benefits from Greenland, half off the GDP of Greenland is subsidies from Denmark, they do not like being treated roughly, when they have supported USA loyally in all it's wars and adventures.