Yes, travel insurance is genuinely useful for a trip to Capri, and the honest reason is access rather than any unusual danger on the island itself. Capri is reached only by ferry or hydrofoil from Naples or Sorrento on the mainland, and both getting there and getting off again in an emergency depend on boats that weather can delay or suspend without much notice. The island itself is genuinely low-risk for the usual reasons travelers worry about; the real exposure is logistical.
The island has a small local clinic for routine care, but anything serious is stabilized there at most and then transferred by boat to Naples, the real medical hub for the region. Confirm your policy covers medical evacuation and transport between the island and the mainland, since that transfer - not treatment on Capri itself - is the part most likely to cost real money.
Capri's summer season, roughly June through September, brings heavy day-tripper crowds and packed ferry schedules that can leave little room to rebook if a sailing is missed or cancelled. Rough seas in the shoulder months of spring and autumn occasionally suspend hydrofoil service outright, stranding visitors on the island or the mainland for a night or more, which is where trip-delay cover earns its keep. Booking flexible ferry tickets where possible reduces the practical risk, but no ticket flexibility replaces a policy that actually pays out for the resulting delay.
Keep any clinic paperwork from Capri or Naples, ferry-cancellation notices, and receipts for unplanned accommodation if a crossing is disrupted. Many policies treat weather-related ferry cancellations as a covered delay rather than a standard claim, so check the wording for how it defines a disrupted crossing before you assume automatic reimbursement for an unplanned night on either side of the water and before your trip begins.