The military argument is complete horseshit. The yanks already have unhindered military access to Greenland. In recent years they have themselves decided to scale down their military presence there to a couple of hundred people at the Thule Airbase. If they wanted to put stuff on Greenland for spying on Russia or early warning systems, the Greenlandic and Danish governments would roll up the red carpet for them.

Regarding minerals, Greenland has comprehensive environmental protections in place to protect the vulnerable Arctic enrichment. Big polluting rare earth refining facilities would not be possible under the current rules. An American invasion could put an unelected occupation government in place that would remove these protections and allow American capital to destroy Greenland for profit.