The Pirate King has been lucky, so far. No losses in bombing Iran. No losses snatching Maduro. If there were no troops in Greenland, that would be another walkover. Even a Brigade of NATO troops, with modern anti-aircraft, anti-tank, and anti-ship, weapons couldn't stop the US, but it would give the US a bloody nose.

My thought was that it isn't whether our nose gets bloodied, but whether any NATO troops get killed.

If there were no NATO troops in Greenland, then no one suffers military casualties. Denmark's got a small force up there (fewer than 200 people), but I don't think Trump cares too much if Denmark gets into a tizzy. As long as we make some kind of effort to seize the area without hurting Danish troops, he might think we can keep a lid on European anger if any of them get injured or killed through inadvertence.

Trump might (mistakenly) think that he can take Greenland that way and only piss off Denmark. Sure, the other NATO allies would get upset - but are they really going to flush the Alliance down the toilet over Greenland? Make American forces leave the Continent over Greenland? Trump might be willing to roll the dice that Europe genuinely doesn't care much about Greenland, and won't give up American security presence there over the abstract concept of Greenland's sovereignty. "We don't like it, but that's what Daddy wanted, so I guess we can live with it."

But if there are French or German troops up there, the stakes are completely different. That equation changes entirely if there are German soldiers coming home in body bags, killed at the hands of Americans. That doesn't get ignored. Engraging Germany carries the risk of losing access to Ramstein and other strategically important assets.