Yes, travel insurance is worth carrying for a trip to Greymouth, and the honest reason has more to do with adventure activity and weather than with any unusual danger on New Zealand's West Coast. Many visitors arrive via the TranzAlpine, the scenic rail journey from Christchurch across the Southern Alps, and that same route matters for insurance: if something serious happens on the West Coast, Christchurch is the realistic hub for more advanced hospital care.
Greymouth has local hospital services for routine treatment, but complex cases are generally referred back across the Alps to Christchurch, and the TranzAlpine's mountain crossing can itself be delayed by snow or slips in the wrong season. Confirm your policy covers medical transfer and transport disruption together, since a delayed rail crossing can complicate an already serious situation.
Whitewater rafting on the West Coast's rivers is a genuine drawcard around Greymouth, and adventure-activity cover is worth checking specifically, since some general policies cap or exclude commercial rafting trips. New Zealand's accident compensation arrangements for visitors form their own separate system with their own rules, which this page cannot summarize accurately for your situation - check how your travel policy interacts with any local accident scheme rather than assuming either one covers everything on its own.
The West Coast sees genuinely heavy rainfall and can flood or slip-close roads with little warning, particularly outside the summer months, so trip-delay cover is worth having regardless of activity plans. Check whether your existing health cover extends abroad and specifically to New Zealand before relying on it.
Keep any clinic paperwork, rafting-operator incident reports, and receipts for delayed rail travel or unplanned accommodation if West Coast weather disrupts your plans. Many policies treat weather-related transport disruption as a standard delay claim, so check the wording for how it is defined before assuming automatic reimbursement.