Yes, travel insurance is worth carrying for a trip through Adelaide's ferry terminal, and the honest reason is less about the city itself, which is a genuinely low-risk, well-equipped Australian capital, and more about what many visitors do next: heading out into the Flinders Ranges or the wider South Australian Outback, where distances and services change dramatically. Many travelers also use Adelaide as the mainland link for a crossing to Kangaroo Island, whose own more limited services are worth planning around.
Adelaide's own hospital care is excellent by any standard, so a city stay alone carries little unusual medical risk. What matters more is whether your own cover actually applies here at all - check whether your existing health cover extends abroad and specifically to Australia before assuming it does, since this varies by country of residence and plan, and the page cannot determine that for you.
Once you leave Adelaide for the Flinders Ranges, the Nullarbor, Kangaroo Island, or the wider Outback, distances between towns grow long and medical services thin out fast, and a breakdown or injury far from a hospital becomes a genuine logistics problem rather than a minor inconvenience. Confirm your policy covers self-drive travel on remote or unsealed roads and any resulting medical transport back to an Adelaide hospital, since standard city-focused cover does not always extend automatically to Outback driving or island travel.
Coastal weather along South Australia's gulf coast can occasionally disrupt ferries and flights in winter, so keep any cancellation notices and receipts for unplanned accommodation if your onward travel is delayed. Keep any clinic paperwork, ranger or police reports, and receipts for treatment or vehicle recovery if something goes wrong further afield, since claims from a remote leg of the trip rely on this kind of documentation far more than a routine city illness would.