Congratulations, the US has probably just sunk the transatlantic part of NATO. There'll probably be some joint European defence agreement (there was before NATO), and the US and Canada will likely have some kind of agreement when missiles become a thing, but not NATO. You've also handed the Soviets the best card for global operations. Why would any country trust the US to come to their aid when they've already demonstrated they'll occupy another country when they want it, making a mockery of it's professed ideals, whilst also trampling over international agreements.
If the US occupies Greenland, then why would any other country allow US bases on their territory unless they were truly unable to defend themselves. Germany has no choice, sure, but what about:
- France, unsure of whether to be a (in their eyes) US puppet by being part of the NATO integrated command and having NATO forces in country. A further push on France already uneasy about NATO.
- Iceland hosted a US base under NATO, which was critical in monitoring Soviet naval movements in to and out of the Atlantic. Why would Iceland continue to tolerate an already controversial US base in Iceland if the US has already occupied Greenland?
Everyone knew that the OTL route was the best route forwards. The Danes know they can't really defend Greenland - there's not enough Danes to do it, given the Soviets across the Baltic and Denmark right in the way of the exit route to the North Sea. However Denmark considers Greenland part of it's home lands - it's settled by Vikings, part of the old Norse area, not some far flung island they've had for a few centuries and already tried to sell a few times (Danish West Indies); it's not acceptable to sell it.
The US gets a near on free military base (if I remember right), without any of the costs or responsibilities for actually looking after the territory whilst respecting their allies. Win for everyone.