Something not mentioned is that Denmark doesn't exactly have a sterling record when it comes to the Inuit. Whatever the situation may be now, that perception may still be there among the Inuit. And if there's going to be a rapid build-up of facilities within the agreed upon boundaries of US installations, it would be good to have something handy until base facilities can handle the increase. And yes, if there is anticipated to be some sort of conflict in the region, one that countries like Denmark may want to sit out, it would be good not to have to rely on their facilities.
In either event, there's no reason to accept the stated reason at face value. Positioning a hospital ship with the rhetoric that it's to help Greenlanders sound a lot better than the other possible reasons. Even "Trump's nuts" works better than "Get ready for war." And if the stated reason sits well with the Inuit, it makes a nice, political, wedge, particularly if long-range plans include annexation of Greenland.