the tldr as to why the US actually does need Greenland...China has cut off the US damn near completely from a number rare earth elements that the US's MIC needs to function. other parts of the world might be willing to start selling researves to the US if they have em or extracting none deposits, but that access does not come free...certainly to an administration hellbent on blatantly extorting anybody and everybody. And if the US's MIC loses it's teeth...well, rest of the world has been tired of the US's warmongering for a long time now.

why greenland specifically?

because greenland just so happens to have an abundance of known REE deposits that are untapped, and is close enough to the US mainland that securing that supply chain would be child's play. but they're not in an easy to mine areas nor does the greenland really have the existing infrastructure to support them. so all around it'd just be a massive endeavor to start exploiting them

why don't they just...ask/bribe their decades long allies to properly start extracting these resources? because they're short-sighted greedy jackals...cruelty is the point with these animals