Especially when the U.S. has a military base there already and has full military cooperation with Denmark/Greenland. The real motivation is pretty clearly resource extraction.
The resource question is a red herring: "Greenlandic ministers have also said their island is “open for business”. But US investors have been slow to show an interest in the nascent mining industry, officials say." (https://www.ft.com/content/c1c8abb1-5c09-46b0-a1d3-68341c4e5...)
We do a lot of important and meaningful work around the world to support democracy, peace and stability. This isn't selfless — it's to create a market for goods and services, and maintain our sphere of influence.
We're so good at shouting the first bit and whispering the latter that voters have come to fully believe it's all charity work, and feel like it's taking bread out of their mouths.
MAGA base and Trump supporters are not rational. It does not matter what Trump is doing or saying, they're "taking their country back" even if they're losing their jobs or benefits. This is downright a cult of personality.
From this perspective Trumps policies are all mostly rational.