Yes, travel insurance matters for a visit to Stanley, and the honest reason is remoteness rather than any specific danger in the town itself. Stanley is the civilian capital of the Falkland Islands, one of the more isolated capitals anywhere, and flights connecting it to the outside world are infrequent, which shapes both the medical and logistical case for coverage more than anything you would encounter walking its streets.
Stanley has its own hospital, King Edward VII Memorial Hospital, which handles general care for residents and visitors, but anything beyond what it can manage typically means evacuation abroad, and depending on the circumstances that has meant transfer to Chile or, for more involved cases, on to the UK. Confirm your policy explicitly covers international medical evacuation from the Falklands specifically, since this is not a destination where a routine local-treatment benefit alone is enough to close the gap.
Many visitors reach Stanley for a single day ashore from an Antarctic-bound or wider South Atlantic cruise, drawn by the wildlife-watching nearby, penguin colonies in particular, that the islands are genuinely known for. A missed reboarding or a delayed tender back to ship is a real practical risk on a cruise stop here, so check that your policy covers missed-departure and trip-disruption scenarios tied to cruise transport specifically, not just standard flight delay, since the two are handled differently by many insurers.
Keep any clinic paperwork from KEMH, cruise-line incident reports, and receipts for unplanned costs if evacuation or a missed departure disrupts your trip. Flight and shipping schedules to the Falklands are infrequent enough that any disruption can mean a genuinely long wait for the next connection, so trip-delay cover is worth confirming carefully rather than assuming quick rebooking is available, and it is worth keeping copies of any booking confirmations as backup documentation.