He also wants the mineral rights to lease to Russia for his own profit? He's also a total idiot, not thinking about the difficulty of mining minerals under 2 miles of ice in extremely remote and difficult terrain.

Trump's role is to be the carnival barker that (apparently) half the U.S. population enjoys watching.

I doubt most of his policies and actions are his ideas. Other people tell him what to do. Notably, he does what Putin tells him to do because Putin owns him. Trump is also owned by several South African billionaires. And he's owned by China.

What do one or more of those entities get out of Trump's obsession with Greenland? Chaos? Destabilization of western allies? Distraction? A genuine interest in controlling Greenland? Russia taunting Denmark?

Trump sees all that land and he wants it - remember, for almost his entire adult life he was a (shady) real estate developer. If he were able somehow to acquire Greenland for the US the new map would tickle his willie more than anything. Greenland also has mining opportunities, but the conditions make mining very difficult. Denmark is not a poor country, and they'd have probably done it already if it made economic sense. But Trump is a moron.

Trump loves his maps!

I don't think either are good reasons to try to take over Greenland of course. But from a purely high level nation state type view, the untapped natural resources and its location make it potentially valuable. Greenland is thought to have a large amount of rare earth metals and its location is close to Arctic shipping routes and potential new routes if the ice continues to melt.

because of its strategic location in the arctic, combined with their minerals needed by both US and Russia. It you look, Greenland is actually closer to Canada than any country, including Denmark, Russia or US.