Since Denmark and Greenland are already NATO allies, the US has pretty much full access to Greenland. The Trump admin says they need it for defence purposes, well, there already is a US base in Greenland and I'm sure the other NATO allies would happily allow the US to expand their presence for defence purposes. Re. the minerals and what's not, also here, the US has pretty much full access. However, there is no company that's interested since digging out those minerals is very difficult and not really worth the investment at this point in time. So, the "I need it" argument is really weak as they already pretty much have it for the purposes they say they want it for.

What is really happening here is part of the Monroe Doctrine [1]. Trump is trying to consolidate the Western Hemisphere. Remember Canada being the 51st state?

[1] https://en.wikipedia.org/wiki/Monroe_Doctrine