Yes, travel insurance is close to essential for a trip to Paamiut, a small settlement on Greenland's southwest coast reachable only by air or sea, with no road connecting it to any other town. The honest core of the answer is distance and weather rather than any dramatic on-the-ground danger - Greenland's towns sit isolated from one another, and getting full hospital treatment from Paamiut means leaving it entirely.
Paamiut has only basic local health services, and anything serious is typically stabilized there if possible and then evacuated to Nuuk, Greenland's capital and the territory's main hospital hub. From Nuuk, genuinely complex or specialist cases are generally referred onward to Denmark, since Greenland's healthcare system is closely tied to the Danish one, though Reykjavik in Iceland can also serve as a nearer link depending on circumstances. Confirm your policy explicitly covers medical evacuation and international repatriation rather than one that only reimburses local clinic visits.
Weather is the practical risk that ties all of this together: small-aircraft service to towns like Paamiut is routinely disrupted by fog, wind, and storms, and a delay of a day or more is a normal occurrence rather than a rare one. This matters as much for a routine departure as it would for an emergency evacuation, so trip-delay cover is worth taking seriously here, not just standard medical benefits.
Keep any clinic paperwork, and receipts for delayed travel or unplanned accommodation if weather disrupts a flight in or out of Paamiut, since documentation is what supports a claim in a place this remote. Check whether your existing health cover extends abroad and specifically to Greenland before you travel, since coverage details vary by country of residence and plan. Many policies require prompt notice before major expenses like evacuation are incurred, so review the claims process before you go rather than after something happens.