The US had military bases in Greenland when Soviet nukes had to be delivered with bombers flying over Greenland.
When ICBMs became a thing, those bases weren't as important anymore.
Something you can already see in Venezuela as we speak: The Trump Administration has essentially blocked countries like Russia and Iran to ship oil from Venezuela.
If they capture Greenland and can build a big Naval presence there they are in a great position to confiscate every cargo ship destined to Russian harbors in the north, and close off China's trading route in the Arctic aswell.
What's the problem? Denmark would have welcomed a big Naval presence in Greenland. It benefits them too.
It should have been:
America: can we have a big Naval base in Greenland?
Denmark: sure. 100 year agreement?
America: give us big Naval base in Greenland or we will annex you!
Denmark: Eh... sure, are you alright?
America: we will annex you.