I understand Greenland is part of the Danish realm.  I lived there (Greenland) for 2 years.  Greenland is solvent.  Alaska is not.  Denmark contributes to the Greenlandic budget to ensure access to their resources.  

You want health and education?  Someone must pay.  In Alaska, no one wants to pay, so health and education suffer.  Denmark "encouraged" Greenlanders to move into the population centers to reduce health and education costs.  Alaska encourages people to settle in the wilderness, off the limited road network, and subsidizing access to modern health and education resources.  

Alaska's welfare model is subsidized by the state, and some cases by the Federal government, at incredible expense to a budget that is no longer capable of supporting it.  Some social programs will have to go, like flying kids to school.