What other choice do they really have? The US has become, to put it politely, entirely unreliable. No nation should be overly dependent on us, and those that are need to diversify ASAP, and there aren't a lot of other options.
I was wondering about that - there is no border really - you seem to drive across and the border patrol folks just asks you nicely - What is the nature of your business?
I don't think America ever said that Greenland would be a state, that it would be an overseas territory of the US instead, which still sucks, but I don't think Trump wants 2 senators and 1 house member from a territory that is bound to be much more liberal than the average American state. Inuits vote Democrat even in Alaska.
Are you absolutely positive? Danes and Germans already sent troops and France a nuclear sub and a Frigate. UK, Sweden, Finland and others are preparing to send troops as well. Perhaps "small operation" is not a foregone conclusion.