Nah, a war with Europe would definitely be bad for many reasons. The US bases inside Europe would be totally fucked.
However, Europe's ability to do more then shake its fist would be limited. They would be unable to project any military force into the Western Hemisphere (Which is where Greenland is lets not forget) to challenge America if it just decides to take the Island. The fact Trump is asking to make a deal for it, is probably a good thing. Denmark could even ask that it receive guaranteed revenues from any successful US business ventures on the Island, or it could just ask for a lump sum. Violence is not necessarily needed here, and at the end of the day is undesirable.
However, despite all the bluster long term (and I am thinking 100 years here), its critical for the USA to secure Greenland. There is no justification for Denmarks control of it beyond that it was a colonial patrimony, and the population of the Island is simply too small to justify self governance given its unique economic and military significance.
Besides, the EU has made "decolonization" of the old European empires a stated goal. Returning Greenland to the American People is part of the decolonization. Its unconscionable that there is still a Colonial outpost with 50,000 Americans on it controlled by a European king. Or does Declonization only mean handing over former possessions to Chinese controlled stooges like Mauritius?
