I think it even makes sense if it were pursued in a different way. Greenland is looking for full independence but can't really hack it financially without aid. I think the COFA (Compact of Free Association) model that we have with Palau and Marshall Islands would work well.
We get expanded military rights and potentially some mineral/drilling rights, while Greenland gets protection, lots of money, access to USPS domestic rates, and probably increased tourism in addition to the independence they desire. Their citizens could also live and work in the US indefinitely.