I’ve seen Greenland used twice under very specific circumstances:  the US counterattack against Germany’s turn 1 Operation Sea Lion using Long Range Aircraft.  If Germany is skilled and lucky, it can effectively eliminate the UK’s chances of recapturing the home island on turn 1 if it can destroy the transport off the coast of Canada.  However, the US can conduct an amphibious assault to try to retake Great Britain on its turn.  Greenland comes into play here by being the one place where a bomber launched from the Eastern US can land after supporting an amphibious assault across the Atlantic into Great Britain.  That’s really the only time I’ve seen Greenland used at all during a game.